%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:19:57 AM UTC 2026 % Result : Unsatisfiable 0.60s 0.72s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL834-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.09/0.36 % Computer : n014.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.02/0.36 % CPULimit : 300 % 0.02/0.36 % WCLimit : 300 % 0.02/0.36 % DateTime : Sun Sep 6 00:09:42 UTC 2026 % 0.02/0.36 % CPUTime : % 0.24/0.52 start to proof:theBenchmark % 0.40/0.66 %------------------------------------------- % 0.40/0.66 % File :CSE---1.7 % 0.40/0.66 % Problem :theBenchmark % 0.40/0.66 % Transform :cnf % 0.40/0.66 % Format :tptp:raw % 0.40/0.66 % Command :java -jar mcs_scs.jar %d %s % 0.40/0.66 % 0.40/0.67 % Result :Theorem 0.023605s % 0.40/0.67 % Output :CNFRefutation 0.023605s % 0.40/0.67 %------------------------------------------- % 0.40/0.67 %------------------------------------------------------------------------------ % 0.40/0.67 % File : LCL834-1 : TPTP v9.3.1. Released v4.1.0. % 0.40/0.67 % Domain : Logic Calculi % 0.40/0.67 % Problem : Strong normalization of typed lambda calculus 228_11 % 0.40/0.67 % Version : Especial. % 0.40/0.67 % English : % 0.40/0.67 % 0.40/0.67 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.40/0.67 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.40/0.67 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.40/0.67 % Source : [Nip10] % 0.40/0.67 % Names : StrongNorm-228_11 [Nip10] % 0.40/0.67 % 0.40/0.67 % Status : Unsatisfiable % 0.40/0.67 % Rating : 0.25 v9.3.0, 0.09 v9.1.0, 0.10 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.30 v5.5.0, 0.45 v5.4.0, 0.40 v5.3.0, 0.39 v5.2.0, 0.31 v5.1.0, 0.41 v5.0.0, 0.36 v4.1.0 % 0.40/0.67 % Syntax : Number of clauses : 472 ( 162 unt; 67 nHn; 260 RR) % 0.40/0.67 % Number of literals : 967 ( 414 equ; 433 neg) % 0.40/0.67 % Maximal clause size : 6 ( 2 avg) % 0.40/0.67 % Maximal term depth : 9 ( 2 avg) % 0.40/0.67 % Number of predicates : 36 ( 35 usr; 0 prp; 1-3 aty) % 0.40/0.67 % Number of functors : 72 ( 72 usr; 22 con; 0-5 aty) % 0.40/0.67 % Number of variables : 1398 ( 209 sgn) % 0.40/0.67 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.40/0.67 % 0.40/0.67 % Comments : % 0.40/0.67 %------------------------------------------------------------------------------ % 0.40/0.67 cnf(cls_App__eq__foldl__conv_5,axiom, % 0.40/0.67 ( V_r != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),V_xa,tc_Lambda_OdB,tc_Lambda_OdB) % 0.40/0.67 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Oappend(V_xa,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_app__last_0,axiom, % 0.40/0.67 hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_App__eq__foldl__conv_3,axiom, % 0.40/0.67 ( c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) % 0.40/0.67 | hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_lists__accD_0,axiom, % 0.40/0.67 ( hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),V_xs)) % 0.40/0.67 | ~ c_List_Olistsp(c_Wellfounded_Oaccp(V_r,T_a),V_xs,T_a) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_rev__replicate_0,axiom, % 0.40/0.67 c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_less__add__eq__less_0,axiom, % 0.40/0.67 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n) % 0.40/0.67 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.40/0.67 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_trans__less__add2_0,axiom, % 0.40/0.67 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.40/0.67 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_trans__less__add1_0,axiom, % 0.40/0.67 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.40/0.67 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_add__lessD1_0,axiom, % 0.40/0.67 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.40/0.67 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.40/0.67 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.40/0.67 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.40/0.67 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.40/0.67 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_map__replicate_0,axiom, % 0.40/0.67 c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_rev__rev__ident_0,axiom, % 0.40/0.67 c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs ). % 0.40/0.67 % 0.40/0.67 cnf(cls_rev__swap_1,axiom, % 0.40/0.67 c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys ). % 0.40/0.67 % 0.40/0.67 cnf(cls_rev__swap_0,axiom, % 0.40/0.67 V_xs = c_List_Orev(c_List_Orev(V_xs,T_a),T_a) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_rotate1__is__Nil__conv_0,axiom, % 0.40/0.67 ( c_List_Orotate1(V_xs,T_a) != c_List_Olist_ONil(T_a) % 0.40/0.67 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_take__eq__Nil_2,axiom, % 0.40/0.67 c_List_Otake(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_replicate__eq__replicate_0,axiom, % 0.40/0.67 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.40/0.67 | V_m = V_n ) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_listsp_ONil_0,axiom, % 0.40/0.67 c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_rev__map_0,axiom, % 0.40/0.67 c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a) ). % 0.40/0.67 % 0.40/0.67 cnf(cls_append__in__listsp__conv_1,axiom, % 0.40/0.67 ( c_List_Olistsp(V_A,V_ys,T_a) % 0.40/0.68 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_append__in__listsp__conv_0,axiom, % 0.40/0.68 ( c_List_Olistsp(V_A,V_xs,T_a) % 0.40/0.68 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_rotate__simps_0,axiom, % 0.40/0.68 c_List_Orotate1(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_Beta_I6_J_0,axiom, % 0.40/0.68 hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_take__map_0,axiom, % 0.40/0.68 c_List_Otake(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Otake(V_n,V_xs,T_b),T_b,T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_order__less__trans_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Opreorder(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_xt1_I10_J_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Oorder(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_last__replicate_0,axiom, % 0.40/0.68 ( c_List_Olast(c_List_Oreplicate(V_n,V_x,T_a),T_a) = V_x % 0.40/0.68 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_uIT_0,axiom, % 0.40/0.68 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_rev__is__Nil__conv_0,axiom, % 0.40/0.68 ( c_List_Orev(V_xs,T_a) != c_List_Olist_ONil(T_a) % 0.40/0.68 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_rev__is__Nil__conv_1,axiom, % 0.40/0.68 c_List_Orev(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_rev__append_0,axiom, % 0.40/0.68 c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_of__nat__aux_Osimps_I1_J_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.40/0.68 | c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_HOL_Ozero__class_Ozero(tc_nat),V_i,T_a) = V_i ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_neq0__conv_1,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_gr0I_0,axiom, % 0.40/0.68 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.40/0.68 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_gr__implies__not0_0,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_not__less0_0,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_replicate__eq__replicate_2,axiom, % 0.40/0.68 c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_replicate__eq__replicate_1,axiom, % 0.40/0.68 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.40/0.68 | V_x = V_y % 0.40/0.68 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_substn_Osimps_I1_J_2,axiom, % 0.40/0.68 ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.40/0.68 | V_i = V_k % 0.40/0.68 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_zero__less__two_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_take__Cons_H_0,axiom, % 0.40/0.68 c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_App__eq__foldl__conv_1,axiom, % 0.40/0.68 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) % 0.40/0.68 | V_ts = c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(V_r,V_s,V_t,V_ts),c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) % 0.40/0.68 | V_ts = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_lists__accI_0,axiom, % 0.40/0.68 ( c_List_Olistsp(c_Wellfounded_Oaccp(V_r,T_a),V_xs,T_a) % 0.40/0.68 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),V_xs)) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_nat__less__le_1,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_less__not__refl_0,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_order__less__le_1,axiom, % 0.40/0.68 ( ~ class_Orderings_Oorder(T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_linorder__neq__iff_1,axiom, % 0.40/0.68 ( ~ class_Orderings_Olinorder(T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_order__less__irrefl_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Opreorder(T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.40/0.68 | V_x = V_y ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Olinorder(T_a) % 0.40/0.68 | V_x = V_y % 0.40/0.68 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_nat__neq__iff_0,axiom, % 0.40/0.68 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.40/0.68 | V_m = V_n ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_nat__less__cases_0,axiom, % 0.40/0.68 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m)) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.40/0.68 | V_m = V_n % 0.40/0.68 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_linorder__neqE__nat_0,axiom, % 0.40/0.68 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.40/0.68 | V_x = V_y ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_linorder__neqE_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Olinorder(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.40/0.68 | V_x = V_y ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_append__replicate__commute_0,axiom, % 0.40/0.68 c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_linorder__less__linear_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Olinorder(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.40/0.68 | V_x = V_y % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.40/0.68 ( ~ class_Orderings_Olinorder(T_a) % 0.40/0.68 | V_x = V_y % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_add__strict__mono_0,axiom, % 0.40/0.68 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_add__less__mono_0,axiom, % 0.40/0.68 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_of__nat__less__iff_1,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_of__nat__less__iff_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_rev__is__rev__conv_0,axiom, % 0.40/0.68 ( c_List_Orev(V_xs,T_a) != c_List_Orev(V_ys,T_a) % 0.40/0.68 | V_xs = V_ys ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_append__in__listsp__conv_2,axiom, % 0.40/0.68 ( c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) % 0.40/0.68 | ~ c_List_Olistsp(V_A,V_ys,T_a) % 0.40/0.68 | ~ c_List_Olistsp(V_A,V_xs,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_shift__gt_0,axiom, % 0.40/0.68 ( hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_Nil__is__rev__conv_0,axiom, % 0.40/0.68 ( c_List_Olist_ONil(T_a) != c_List_Orev(V_xs,T_a) % 0.40/0.68 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_ex__least__nat__less_0,axiom, % 0.40/0.68 ( c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(V_P,V_n),V_n,tc_nat) % 0.40/0.68 | ~ hBOOL(hAPP(V_P,V_n)) % 0.40/0.68 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_power__strict__increasing__iff_1,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_power__strict__increasing__iff_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_power__strict__increasing_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_power__less__imp__less__exp_0,axiom, % 0.40/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.68 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.40/0.68 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_not__add__less1_0,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_not__add__less2_0,axiom, % 0.40/0.68 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_type_Osimps_I2_J_1,axiom, % 0.40/0.68 ( c_Type_Otype_OFun(V_type1,V_type2) != c_Type_Otype_OFun(V_type1_H,V_type2_H) % 0.40/0.68 | V_type2 = V_type2_H ) ). % 0.40/0.68 % 0.40/0.68 cnf(cls_type_Osimps_I2_J_0,axiom, % 0.40/0.68 ( c_Type_Otype_OFun(V_type1,V_type2) != c_Type_Otype_OFun(V_type1_H,V_type2_H) % 0.40/0.68 | V_type1 = V_type1_H ) ). % 0.40/0.68 % 0.40/0.69 cnf(cls_add__strict__right__mono_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__less__cancel__right_1,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__less__cancel__right_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__strict__left__mono_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__less__cancel__left_1,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__less__cancel__left_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__less__mono1_0,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_nat__add__left__cancel__less_0,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_nat__add__left__cancel__less_1,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_butlast_Osimps_I1_J_0,axiom, % 0.40/0.69 c_List_Obutlast(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_Nil__is__rev__conv_1,axiom, % 0.40/0.69 c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_xt1_I9_J_0,axiom, % 0.40/0.69 ( ~ class_Orderings_Oorder(T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.40/0.69 ( ~ class_Orderings_Olinorder(T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_order__less__asym_0,axiom, % 0.40/0.69 ( ~ class_Orderings_Opreorder(T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_order__less__asym_H_0,axiom, % 0.40/0.69 ( ~ class_Orderings_Opreorder(T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_power__strict__decreasing_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_one__less__power_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_append__butlast__last__id_0,axiom, % 0.40/0.69 ( c_List_Oappend(c_List_Obutlast(V_xs,T_a),c_List_Olist_OCons(c_List_Olast(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a) = V_xs % 0.40/0.69 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__neg__neg_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_even__less__0__iff_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_even__less__0__iff_1,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__pos__pos_0,axiom, % 0.40/0.69 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_pos__add__strict_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_not__one__less__zero_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_zero__less__one_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_less__add__one_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_zero__less__power_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_replicate__empty_1,axiom, % 0.40/0.69 c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_take__eq__Nil_0,axiom, % 0.40/0.69 ( c_List_Otake(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a) % 0.40/0.69 | V_xs = c_List_Olist_ONil(T_a) % 0.40/0.69 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_empty__replicate_1,axiom, % 0.40/0.69 c_List_Olist_ONil(T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_take__0_0,axiom, % 0.40/0.69 c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_replicate__empty_0,axiom, % 0.40/0.69 ( c_List_Oreplicate(V_n,V_x,T_a) != c_List_Olist_ONil(T_a) % 0.40/0.69 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_empty__replicate_0,axiom, % 0.40/0.69 ( c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a) % 0.40/0.69 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_singleton__rev__conv_1,axiom, % 0.40/0.69 c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_last_Osimps_1,axiom, % 0.40/0.69 ( c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a) % 0.40/0.69 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_rev__singleton__conv_1,axiom, % 0.40/0.69 c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_singleton__rev__conv_0,axiom, % 0.40/0.69 ( c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) != c_List_Orev(V_xs,T_a) % 0.40/0.69 | V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_rev__singleton__conv_0,axiom, % 0.40/0.69 ( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) % 0.40/0.69 | V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_butlast_Osimps_I2_J_0,axiom, % 0.40/0.69 c_List_Obutlast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_last_Osimps_0,axiom, % 0.40/0.69 c_List_Olast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = V_x ). % 0.40/0.69 % 0.40/0.69 cnf(cls_butlast_Osimps_I2_J_1,axiom, % 0.40/0.69 ( c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a) % 0.40/0.69 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__gr__0_1,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__gr__0_2,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_add__gr__0_0,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.40/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_append__eq__Cons__conv_3,axiom, % 0.40/0.69 ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a) % 0.40/0.69 | c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) = V_xs % 0.40/0.69 | V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_Cons__eq__append__conv_2,axiom, % 0.40/0.69 ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a) % 0.40/0.69 | c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) = V_ys % 0.40/0.69 | c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_append__eq__Cons__conv_2,axiom, % 0.40/0.69 ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a) % 0.40/0.69 | V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) % 0.40/0.69 | V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_Cons__eq__append__conv_3,axiom, % 0.40/0.69 ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a) % 0.40/0.69 | V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) % 0.40/0.69 | c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_replicate__app__Cons__same_0,axiom, % 0.40/0.69 c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_power__inject__exp_0,axiom, % 0.40/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.40/0.69 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 0.40/0.69 | V_m = V_n ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_butlast__append_0,axiom, % 0.40/0.69 c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Obutlast(V_xs,T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_last__append_1,axiom, % 0.40/0.69 ( c_List_Olast(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Olast(V_ys,T_a) % 0.40/0.69 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_last__append_0,axiom, % 0.40/0.69 c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olast(V_xs,T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_butlast__append_1,axiom, % 0.40/0.69 ( c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(V_xs,c_List_Obutlast(V_ys,T_a),T_a) % 0.40/0.69 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_replicate__add_0,axiom, % 0.40/0.69 c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_App_0,axiom, % 0.40/0.69 ( c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) % 0.40/0.69 | ~ c_Type_Otyping(V_env,V_t,V_T) % 0.40/0.69 | ~ c_Type_Otyping(V_env,V_s,c_Type_Otype_OFun(V_T,V_U)) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_subst__Var_1,axiom, % 0.40/0.69 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.40/0.69 | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x) = V_s ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_subst__Var_2,axiom, % 0.40/0.69 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k) = c_Lambda_OdB_OVar(V_i) % 0.40/0.69 | V_i = V_k % 0.40/0.69 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_subst__lt_0,axiom, % 0.40/0.69 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i) = c_Lambda_OdB_OVar(V_j) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.40/0.69 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(V_i) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_liftn_Osimps_I1_J_0,axiom, % 0.40/0.69 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.40/0.69 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_Cons__eq__append__conv_1,axiom, % 0.40/0.69 ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a) % 0.40/0.69 | V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) % 0.40/0.69 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.40/0.69 % 0.40/0.69 cnf(cls_append__eq__Cons__conv_0,axiom, % 0.40/0.69 ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a) % 0.40/0.69 | V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) % 0.40/0.69 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_last__snoc_0,axiom, % 0.40/0.70 c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_x ). % 0.40/0.70 % 0.40/0.70 cnf(cls_butlast__snoc_0,axiom, % 0.40/0.70 c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_xs ). % 0.40/0.70 % 0.40/0.70 cnf(cls_append__eq__Cons__conv_1,axiom, % 0.40/0.70 ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a) % 0.40/0.70 | c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) = V_xs % 0.40/0.70 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_Cons__eq__append__conv_0,axiom, % 0.40/0.70 ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a) % 0.40/0.70 | c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) = V_ys % 0.40/0.70 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_rev_Osimps_I2_J_0,axiom, % 0.40/0.70 c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_rev__eq__Cons__iff_0,axiom, % 0.40/0.70 ( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a) % 0.40/0.70 | V_xs = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_rev__eq__Cons__iff_1,axiom, % 0.40/0.70 c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_rotate__simps_1,axiom, % 0.40/0.70 c_List_Orotate1(c_List_Olist_OCons(V_x,V_xs,T_b),T_b) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_b),T_b),T_b) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_replicate__append__same_0,axiom, % 0.40/0.70 c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_take__1__Cons_0,axiom, % 0.40/0.70 c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_ex__least__nat__less_2,axiom, % 0.40/0.70 ( hBOOL(hAPP(V_P,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1(V_P,V_n)),c_HOL_Oone__class_Oone(tc_nat)))) % 0.40/0.70 | ~ hBOOL(hAPP(V_P,V_n)) % 0.40/0.70 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_Cons__acc__step1I_0,axiom, % 0.40/0.70 ( hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))) % 0.40/0.70 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_ListOrder_Ostep1(V_r,T_a),tc_List_Olist(T_a)),V_xs)) % 0.40/0.70 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_x)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_liftn_Osimps_I1_J_1,axiom, % 0.40/0.70 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n)) % 0.40/0.70 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_IT_OVar_0,axiom, % 0.40/0.70 ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.40/0.70 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_lift__subst__lt_0,axiom, % 0.40/0.70 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat))) % 0.40/0.70 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_lift__subst_0,axiom, % 0.40/0.70 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j) % 0.40/0.70 | ~ c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_lift_Osimps_I1_J_1,axiom, % 0.40/0.70 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat))) % 0.40/0.70 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_Abs_0,axiom, % 0.40/0.70 ( c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),c_Type_Otype_OFun(V_T,V_U)) % 0.40/0.70 | ~ c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_uT_0,axiom, % 0.40/0.70 c_Type_Otyping(v_e____,v_u____,v_T____) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_Beta_I7_J_0,axiom, % 0.40/0.70 c_Type_Otyping(v_ea______,v_ua______,v_T____) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_substn_Osimps_I1_J_1,axiom, % 0.40/0.70 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.40/0.70 | c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x) = c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_semiring__1__class_Oof__nat__code_0,axiom, % 0.40/0.70 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.40/0.70 | c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) = c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a),T_a,T_a,T_a),V_n,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_lift__types_0,axiom, % 0.40/0.70 ( c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) % 0.40/0.70 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_MI2_0,axiom, % 0.40/0.70 ( v_T____ != c_Type_Otype_OFun(V_T1,V_T2) % 0.40/0.70 | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i))) % 0.40/0.70 | ~ c_Type_Otyping(V_e,V_u,V_T2) % 0.40/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.40/0.70 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta) % 0.40/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_MI1_0,axiom, % 0.40/0.70 ( v_T____ != c_Type_Otype_OFun(V_T1,V_T2) % 0.40/0.70 | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i))) % 0.40/0.70 | ~ c_Type_Otyping(V_e,V_u,V_T1) % 0.40/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.40/0.70 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta) % 0.40/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_lifts__IT_0,axiom, % 0.40/0.70 ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) % 0.40/0.70 | ~ c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_apps__betasE_10,axiom, % 0.40/0.70 ( V_rs = c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB) % 0.40/0.70 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.40/0.70 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_apps__betasE_4,axiom, % 0.40/0.70 ( V_rs = c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB) % 0.40/0.70 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.40/0.70 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s))) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_substs__lemma_0,axiom, % 0.40/0.70 ( c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) % 0.40/0.70 | ~ c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts) % 0.40/0.70 | ~ c_Type_Otyping(V_e,V_u,V_T) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_apps__betasE_1,axiom, % 0.40/0.70 ( V_rs = c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB) % 0.40/0.70 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s))) % 0.40/0.70 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s))) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_apps__betasE_7,axiom, % 0.40/0.70 ( V_rs = c_List_Olist_OCons(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB) % 0.40/0.70 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s))) % 0.40/0.70 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_COMBC__def_0,axiom, % 0.40/0.70 hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_map__is__Nil__conv_1,axiom, % 0.40/0.70 c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_of__nat__1_0,axiom, % 0.40/0.70 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.40/0.70 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_rtranclp__converseD_0,axiom, % 0.40/0.70 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_rtranclp__converseI_0,axiom, % 0.40/0.70 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_Snoc__step1__SnocD_1,axiom, % 0.40/0.70 ( hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.40/0.70 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)) % 0.40/0.70 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a))) ) ). % 0.40/0.70 % 0.40/0.70 cnf(cls_typing_OVar_0,axiom, % 0.40/0.70 c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ). % 0.40/0.70 % 0.60/0.70 cnf(cls_append__eq__Cons__conv_5,axiom, % 0.60/0.70 c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_append__Cons_0,axiom, % 0.60/0.70 c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_map__eq__Cons__conv_3,axiom, % 0.60/0.70 c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Cons__eq__map__conv_3,axiom, % 0.60/0.70 c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_map_Osimps_I2_J_0,axiom, % 0.60/0.70 c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_natgb_Oadd__cancel_0,axiom, % 0.60/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z) % 0.60/0.70 | V_y = V_z ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_nat__add__right__cancel_0,axiom, % 0.60/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k) % 0.60/0.70 | V_m = V_n ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_nat__add__left__cancel_0,axiom, % 0.60/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n) % 0.60/0.70 | V_m = V_n ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.60/0.70 | ~ class_Int_Onumber__ring(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) % 0.60/0.70 | V_y = V_z ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__imp__eq_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) % 0.60/0.70 | V_b = V_c ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__left__cancel_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) % 0.60/0.70 | V_b = V_c ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__right__cancel_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) % 0.60/0.70 | V_b = V_c ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Cons__eq__append__conv_5,axiom, % 0.60/0.70 c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Cons__eq__appendI_0,axiom, % 0.60/0.70 c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_neq__Nil__conv_1,axiom, % 0.60/0.70 c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_list_Osimps_I3_J_0,axiom, % 0.60/0.70 c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Cons__step1__Cons_0,axiom, % 0.60/0.70 ( V_x = V_y % 0.60/0.70 | hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_subject__reduction_H_0,axiom, % 0.60/0.70 ( c_Type_Otyping(V_e,V_t_H,V_T) % 0.60/0.70 | ~ c_Type_Otyping(V_e,V_t,V_T) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_not__Cons__self2_0,axiom, % 0.60/0.70 c_List_Olist_OCons(V_x,V_t,T_a) != V_t ). % 0.60/0.70 % 0.60/0.70 cnf(cls_not__Cons__self_0,axiom, % 0.60/0.70 V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Cons__eq__append__conv_4,axiom, % 0.60/0.70 c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_app__Var__IT_0,axiom, % 0.60/0.70 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))) % 0.60/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_subst__lemma_0,axiom, % 0.60/0.70 ( ~ c_Type_Otyping(V_e_H,V_u,V_U) % 0.60/0.70 | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T) % 0.60/0.70 | c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Nil__is__map__conv_1,axiom, % 0.60/0.70 c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Snoc__step1__SnocD_0,axiom, % 0.60/0.70 ( V_ys = V_xs % 0.60/0.70 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a))) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Nil__is__append__conv_2,axiom, % 0.60/0.70 c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_rtranclp__idemp_0,axiom, % 0.60/0.70 c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_monoid__add_Oadd__0__right_0,axiom, % 0.60/0.70 ( hAPP(hAPP(V_plus,V_a),V_zero) = V_a % 0.60/0.70 | ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_monoid__add_Oadd__0__left_0,axiom, % 0.60/0.70 ( hAPP(hAPP(V_plus,V_zero),V_a) = V_a % 0.60/0.70 | ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_apps__betasE_8,axiom, % 0.60/0.70 ( V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.70 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s))) % 0.60/0.70 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_apps__betasE_2,axiom, % 0.60/0.70 ( V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.70 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s))) % 0.60/0.70 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s))) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_power__eq__0__iff_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.60/0.70 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.60/0.70 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.60/0.70 | ~ class_Power_Opower(T_a) % 0.60/0.70 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.60/0.70 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_field__power__not__zero_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 0.60/0.70 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.60/0.70 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_one__neq__zero_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.60/0.70 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_double__eq__0__iff_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.60/0.70 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.60/0.70 | ~ class_Int_Onumber__ring(T_a) % 0.60/0.70 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a) % 0.60/0.70 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_double__eq__0__iff_1,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_zero__neq__one_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.60/0.70 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Oadd__0_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.60/0.70 | ~ class_Int_Onumber__ring(T_a) % 0.60/0.70 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__0__left_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_power__0__left_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.60/0.70 | ~ class_Power_Opower(T_a) % 0.60/0.70 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_liftn__0_0,axiom, % 0.60/0.70 c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__is__0_1,axiom, % 0.60/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.60/0.70 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__is__0_0,axiom, % 0.60/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.60/0.70 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 0.60/0.70 ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a) % 0.60/0.70 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__eq__self__zero_0,axiom, % 0.60/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m % 0.60/0.70 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__is__0_2,axiom, % 0.60/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 0.60/0.70 V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_plus__nat_Oadd__0_0,axiom, % 0.60/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ). % 0.60/0.70 % 0.60/0.70 cnf(cls_Nat_Oadd__0__right_0,axiom, % 0.60/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ). % 0.60/0.70 % 0.60/0.70 cnf(cls_dB_Osplit__asm_1,axiom, % 0.60/0.70 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a))) % 0.60/0.70 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc))) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_dB_Osplit_1,axiom, % 0.60/0.70 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a))) % 0.60/0.70 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2))) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.60/0.70 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_power__one_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.60/0.70 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_dB_Osimps_I10_J_0,axiom, % 0.60/0.70 c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_add__cancel__21_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_conversepD_0,axiom, % 0.60/0.70 ( hBOOL(hAPP(hAPP(V_r,V_b),V_a)) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_conversep__iff_1,axiom, % 0.60/0.70 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_conversep_Ocases_0,axiom, % 0.60/0.70 ( hBOOL(hAPP(hAPP(V_r,V_a2),V_a1)) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_conversep_Ointros_0,axiom, % 0.60/0.70 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a)) % 0.60/0.70 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 0.60/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 0.60/0.70 % 0.60/0.70 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 0.60/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.60/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ). % 0.60/0.70 % 0.60/0.71 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_nat__add__assoc_0,axiom, % 0.60/0.71 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_nat__add__left__commute_0,axiom, % 0.60/0.71 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_add__cancel__21_1,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_class__semiring_Oadd__a_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__step1I_0,axiom, % 0.60/0.71 ( ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_ys,V_x,T_a)),c_List_Oappend(V_xs,V_x,T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__step1I_1,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_x,V_vs,T_a)),c_List_Oappend(V_x,V_us,T_a))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_vs),V_us)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Cons__step1__Cons_2,axiom, % 0.60/0.71 ( V_x = V_y % 0.60/0.71 | V_xs = V_ys % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Cons__step1__Cons_4,axiom, % 0.60/0.71 ( ~ hBOOL(hAPP(hAPP(V_r,V_y),V_xa)) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_x,T_a)),c_List_Olist_OCons(V_xa,V_x,T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__same__eq_0,axiom, % 0.60/0.71 ( c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a) % 0.60/0.71 | V_ys = V_zs ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_same__append__eq_0,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a) % 0.60/0.71 | V_ys = V_zs ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtranclp_Ortrancl__refl_0,axiom, % 0.60/0.71 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Nitpick_Ortranclp__def_1,axiom, % 0.60/0.71 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_accp__downwards_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_b)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) % 0.60/0.71 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_accp__downwards__aux_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_b)) % 0.60/0.71 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtranclp__trans_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_IT__implies__termi_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t)) % 0.60/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_termi__implies__IT_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,V_r)) % 0.60/0.71 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_r)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__Nil2_0,axiom, % 0.60/0.71 c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ). % 0.60/0.71 % 0.60/0.71 cnf(cls_eq__Nil__appendI_0,axiom, % 0.60/0.71 V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_self__append__conv_1,axiom, % 0.60/0.71 V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__Nil_0,axiom, % 0.60/0.71 c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ). % 0.60/0.71 % 0.60/0.71 cnf(cls_self__append__conv2_1,axiom, % 0.60/0.71 V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_substn_Osimps_I3_J_0,axiom, % 0.60/0.71 c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_nat__add__commute_0,axiom, % 0.60/0.71 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Snoc__step1__SnocD_3,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.60/0.71 | V_y = V_x % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_of__nat__eq__iff_0,axiom, % 0.60/0.71 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.60/0.71 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.60/0.71 | V_m = V_n ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_typing__elims_I1_J_0,axiom, % 0.60/0.71 ( hAPP(V_e,V_i) = V_T % 0.60/0.71 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Nil__is__map__conv_0,axiom, % 0.60/0.71 ( c_List_Olist_ONil(T_a) != c_List_Omap(V_f,V_xs,T_b,T_a) % 0.60/0.71 | V_xs = c_List_Olist_ONil(T_b) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Var__IT_0,axiom, % 0.60/0.71 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_power__one__right_0,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_r__into__rtranclp_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_not__Nil__step1_0,axiom, % 0.60/0.71 ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_ONil(T_a)),V_xs)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_not__step1__Nil_0,axiom, % 0.60/0.71 ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_xs),c_List_Olist_ONil(T_a))) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_shift__eq_0,axiom, % 0.60/0.71 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift__IT_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i))) % 0.60/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Nil__is__append__conv_0,axiom, % 0.60/0.71 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) % 0.60/0.71 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Nil__is__append__conv_1,axiom, % 0.60/0.71 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) % 0.60/0.71 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__is__Nil__conv_0,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) % 0.60/0.71 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__is__Nil__conv_1,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) % 0.60/0.71 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_conversep__eq_0,axiom, % 0.60/0.71 c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Orecs_I1_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift__preserves__beta_H_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Cons__step1__Cons_3,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)) % 0.60/0.71 | V_xs = V_ys % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_semigroup__add_Oadd__assoc_0,axiom, % 0.60/0.71 ( hAPP(hAPP(V_plus,hAPP(hAPP(V_plus,V_a),V_b)),V_c) = hAPP(hAPP(V_plus,V_a),hAPP(hAPP(V_plus,V_b),V_c)) % 0.60/0.71 | ~ c_OrderedGroup_Osemigroup__add(V_plus,T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_liftn_Osimps_I3_J_0,axiom, % 0.60/0.71 c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_map__append_0,axiom, % 0.60/0.71 c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_list_Osimps_I2_J_0,axiom, % 0.60/0.71 c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Snoc__step1__SnocD_2,axiom, % 0.60/0.71 ( V_ys = V_xs % 0.60/0.71 | V_y = V_x % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift__map_0,axiom, % 0.60/0.71 hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_power__0_0,axiom, % 0.60/0.71 ( ~ class_Power_Opower(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_class__semiring_Opwr__0_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_semigroup__add__class_Oaxioms_0,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Osemigroup__add(T_a) % 0.60/0.71 | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__Var__IT_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j))) % 0.60/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_conversep__conversep_0,axiom, % 0.60/0.71 c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__self__conv_0,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,V_ys,T_a) != V_xs % 0.60/0.71 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_self__append__conv_0,axiom, % 0.60/0.71 ( V_xs != c_List_Oappend(V_xs,V_ys,T_a) % 0.60/0.71 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__self__conv2_0,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,V_ys,T_a) != V_ys % 0.60/0.71 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_self__append__conv2_0,axiom, % 0.60/0.71 ( V_ys != c_List_Oappend(V_xs,V_ys,T_a) % 0.60/0.71 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__eq__Cons__conv_4,axiom, % 0.60/0.71 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_list_Oinject_0,axiom, % 0.60/0.71 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) % 0.60/0.71 | V_a = V_a_H ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_list_Oinject_1,axiom, % 0.60/0.71 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) % 0.60/0.71 | V_list = V_list_H ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Cons__step1__Cons_1,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)) % 0.60/0.71 | hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_y,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Cons__step1__Cons_5,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),c_List_Olist_OCons(V_x,V_ys,T_a)),c_List_Olist_OCons(V_x,V_xs,T_a))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(V_r,T_a),V_ys),V_xs)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osplit_0,axiom, % 0.60/0.71 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a))) % 0.60/0.71 | hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osplit__asm_0,axiom, % 0.60/0.71 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a))) % 0.60/0.71 | hBOOL(hAPP(V_P,hAPP(V_f1,V_xd))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.60/0.71 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.60/0.71 | V_nat = V_nat_H ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_of__nat__add_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.60/0.71 | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_map__is__Nil__conv_0,axiom, % 0.60/0.71 ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_ONil(T_a) % 0.60/0.71 | V_xs = c_List_Olist_ONil(T_b) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append1__eq__conv_0,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) % 0.60/0.71 | V_xs = V_ys ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append1__eq__conv_1,axiom, % 0.60/0.71 ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) % 0.60/0.71 | V_x = V_y ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__is__Nil__conv_2,axiom, % 0.60/0.71 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift_Osimps_I3_J_0,axiom, % 0.60/0.71 hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__assoc_0,axiom, % 0.60/0.71 c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__eq__appendI_0,axiom, % 0.60/0.71 c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__eq__append__conv2_4,axiom, % 0.60/0.71 c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_append__eq__append__conv2_5,axiom, % 0.60/0.71 c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_SI2_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_i))) % 0.60/0.71 | ~ c_Type_Otyping(V_e,V_u,v_T____) % 0.60/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.60/0.71 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift__type_0,axiom, % 0.60/0.71 ( c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T) % 0.60/0.71 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_converse__rtranclp__into__rtranclp_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_accp_Ocases_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_y)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a)) % 0.60/0.71 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_accp__downward_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_a)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) % 0.60/0.71 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(V_r,T_a),V_b)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.60/0.71 hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osimps_I11_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Orecs_I2_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_liftn_Osimps_I2_J_0,axiom, % 0.60/0.71 c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_substn_Osimps_I2_J_0,axiom, % 0.60/0.71 c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.60/0.71 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_6,axiom, % 0.60/0.71 ( V_u = hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u))) % 0.60/0.71 | V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_5,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))) % 0.60/0.71 | V_u = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t) % 0.60/0.71 | V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_4,axiom, % 0.60/0.71 ( V_u = hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)) % 0.60/0.71 | V_u = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t) % 0.60/0.71 | V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_7,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u))) % 0.60/0.71 | V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_substn__subst__n_0,axiom, % 0.60/0.71 c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subject__reduction_0,axiom, % 0.60/0.71 ( c_Type_Otyping(V_e,V_t_H,V_T) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) % 0.60/0.71 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I1_J_0,axiom, % 0.60/0.71 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_lift__preserves__beta_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__Abs_0,axiom, % 0.60/0.71 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_apps__betasE_5,axiom, % 0.60/0.71 ( V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_apps__betasE_11,axiom, % 0.60/0.71 ( V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4(V_r,V_rs,V_s)),c_HOL_Ozero__class_Ozero(tc_nat)),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osplit__asm_2,axiom, % 0.60/0.71 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a))) % 0.60/0.71 | hBOOL(hAPP(V_P,hAPP(V_f3,V_xa))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osplit_2,axiom, % 0.60/0.71 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a))) % 0.60/0.71 | hBOOL(hAPP(V_P,hAPP(V_f3,V_dB))) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Orecs_I3_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_dB_Osimps_I12_J_0,axiom, % 0.60/0.71 c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Lambda_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) % 0.60/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_apps__betasE_0,axiom, % 0.60/0.71 ( V_r = c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s))) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_apps__betasE_6,axiom, % 0.60/0.71 ( V_r = c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s))) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_head__Var__reduction_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_var__app__type__eq_0,axiom, % 0.60/0.71 ( V_T = V_U % 0.60/0.71 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U) % 0.60/0.71 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Var__eq__apps__conv_2,axiom, % 0.60/0.71 c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_App__eq__foldl__conv_2,axiom, % 0.60/0.71 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_r = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(V_r,V_s,V_t,V_ts),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_ts = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_ex__head__tail_0,axiom, % 0.60/0.71 V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Var__eq__apps__conv_1,axiom, % 0.60/0.71 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_semigroup__add_Ofoldl__assoc_0,axiom, % 0.60/0.71 ( c_List_Ofoldl(V_plus,hAPP(hAPP(V_plus,V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_y,V_zs,T_a,T_a)) % 0.60/0.71 | ~ c_OrderedGroup_Osemigroup__add(V_plus,T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_foldl__Nil_0,axiom, % 0.60/0.71 c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ). % 0.60/0.71 % 0.60/0.71 cnf(cls_foldl__assoc_0,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Osemigroup__add(T_a) % 0.60/0.71 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_monoid__add_Ofoldl__absorb0_0,axiom, % 0.60/0.71 ( hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_zero,V_zs,T_a,T_a)) = c_List_Ofoldl(V_plus,V_x,V_zs,T_a,T_a) % 0.60/0.71 | ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_foldl__Cons_0,axiom, % 0.60/0.71 c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_foldl__append_0,axiom, % 0.60/0.71 c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__map_0,axiom, % 0.60/0.71 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__eq_0,axiom, % 0.60/0.71 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__lift_0,axiom, % 0.60/0.71 hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Beta_I5_J_0,axiom, % 0.60/0.71 c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_T_0,axiom, % 0.60/0.71 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_1,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))) % 0.60/0.71 | V_u = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t) % 0.60/0.71 | V_u = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_2,axiom, % 0.60/0.71 ( V_u = hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u))) % 0.60/0.71 | V_u = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_3,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u))) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u))) % 0.60/0.71 | V_u = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I3_J_0,axiom, % 0.60/0.71 ( V_u = hAPP(hAPP(c_Lambda_OdB_OApp,V_s),c_Lambda_Osko__Lambda__Xbeta__cases__3__3(V_s,V_t,V_u)) % 0.60/0.71 | V_u = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osko__Lambda__Xbeta__cases__3__2(V_s,V_t,V_u)),V_t) % 0.60/0.71 | V_u = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Osko__Lambda__Xbeta__cases__3__1(V_s,V_t,V_u)),V_t),c_HOL_Ozero__class_Ozero(tc_nat)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_u)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_apps__betasE_9,axiom, % 0.60/0.71 ( V_r = c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_apps__betasE_3,axiom, % 0.60/0.71 ( V_r = c_Lambda_OdB_OAbs(c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3(V_r,V_rs,V_s)) % 0.60/0.71 | V_s = c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2(V_r,V_rs,V_s),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1(V_r,V_rs,V_s))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Beta_I3_J_0,axiom, % 0.60/0.71 hBOOL(hAPP(c_InductTermi_OIT,v_a____)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_head__Var__reduction_1,axiom, % 0.60/0.71 ( V_v = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_power__eq__0__iff_2,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.60/0.71 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.60/0.71 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.60/0.71 | ~ class_Power_Opower(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.60/0.71 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_power__0__left_1,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.60/0.71 | ~ class_Power_Opower(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.60/0.71 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_power__eq__0__iff_1,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.60/0.71 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.60/0.71 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.60/0.71 | ~ class_Power_Opower(T_a) % 0.60/0.71 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_of__nat__0_0,axiom, % 0.60/0.71 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.60/0.71 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_foldl__absorb0_0,axiom, % 0.60/0.71 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.60/0.71 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtrancl__beta__AppR_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtrancl__beta__AppL_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtrancl__beta__App_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_substn__subst__0_0,axiom, % 0.60/0.71 c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I2_J_1,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_rtrancl__beta__Abs_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_beta__cases_I2_J_0,axiom, % 0.60/0.71 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_App__eq__foldl__conv_4,axiom, % 0.60/0.71 hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom, % 0.60/0.71 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_m = V_n ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom, % 0.60/0.71 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | V_rs = V_ss ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_App__eq__foldl__conv_0,axiom, % 0.60/0.71 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_Var__eq__apps__conv_0,axiom, % 0.60/0.71 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.71 | c_Lambda_OdB_OVar(V_m) = V_s ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__preserves__beta2_H_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.60/0.71 % 0.60/0.71 cnf(cls_subst__preserves__beta_H_0,axiom, % 0.60/0.71 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))) % 0.60/0.71 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.60/0.71 % 0.60/0.72 cnf(cls_subst__preserves__beta2_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_SI1_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i))) % 0.60/0.72 | ~ c_Type_Otyping(V_e,V_u,v_T____) % 0.60/0.72 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.60/0.72 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_double__induction__lemma_0,axiom, % 0.60/0.72 ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.60/0.72 | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_s)) % 0.60/0.72 | hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__preserves__beta2_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__preserves__betas_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_ListOrder_Ostep1(c_Lambda_Obeta,tc_Lambda_OdB),V_rs),V_ss)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Abs__eq__apps__conv_1,axiom, % 0.60/0.72 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.72 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Var__apps__neq__Abs__apps_0,axiom, % 0.60/0.72 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Abs__eq__apps__conv_2,axiom, % 0.60/0.72 c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__eq__Abs__conv_1,axiom, % 0.60/0.72 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.60/0.72 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__eq__Abs__conv_2,axiom, % 0.60/0.72 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Abs__App__neq__Var__apps_0,axiom, % 0.60/0.72 hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_IT_OBeta_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.60/0.72 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s)) % 0.60/0.72 | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Beta_I1_J_0,axiom, % 0.60/0.72 hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_subst__App_0,axiom, % 0.60/0.72 hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.60/0.72 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.60/0.72 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__eq__Abs__conv_0,axiom, % 0.60/0.72 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.60/0.72 | V_s = c_Lambda_OdB_OAbs(V_r) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom, % 0.60/0.72 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.72 | V_r = V_s ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom, % 0.60/0.72 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.72 | V_rs = V_ss ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.60/0.72 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.60/0.72 | V_dB1 = V_dB1_H ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.60/0.72 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.60/0.72 | V_dB2 = V_dB2_H ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_beta_0,axiom, % 0.60/0.72 hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__preserves__beta_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.60/0.72 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.60/0.72 | V_dB = V_dB_H ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_subst__preserves__beta_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_Abs__eq__apps__conv_0,axiom, % 0.60/0.72 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.72 | c_Lambda_OdB_OAbs(V_r) = V_s ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_apps__eq__tail__conv_0,axiom, % 0.60/0.72 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) % 0.60/0.72 | V_r = V_s ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_appR_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_appL_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_abs_0,axiom, % 0.60/0.72 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t))) % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_conjecture_0,negated_conjecture, % 0.60/0.72 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_fun__Orderings_Opreorder,axiom, % 0.60/0.72 ( class_Orderings_Opreorder(tc_fun(T_2,T_1)) % 0.60/0.72 | ~ class_Orderings_Opreorder(T_1) ) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_fun__Orderings_Oorder,axiom, % 0.60/0.72 ( class_Orderings_Oorder(tc_fun(T_2,T_1)) % 0.60/0.72 | ~ class_Orderings_Oorder(T_1) ) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 0.60/0.72 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 0.60/0.72 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 0.60/0.72 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 0.60/0.72 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 0.60/0.72 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 0.60/0.72 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.60/0.72 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.60/0.72 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 0.60/0.72 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 0.60/0.72 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 0.60/0.72 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom, % 0.60/0.72 class_OrderedGroup_Osemigroup__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.60/0.72 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 0.60/0.72 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 0.60/0.72 class_Ring__and__Field_Omult__zero(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 0.60/0.72 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 0.60/0.72 class_OrderedGroup_Omonoid__add(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.60/0.72 class_Nat_Osemiring__char__0(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.60/0.72 class_Orderings_Opreorder(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.60/0.72 class_Orderings_Olinorder(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.60/0.72 class_Orderings_Oorder(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_nat__Power_Opower,axiom, % 0.60/0.72 class_Power_Opower(tc_nat) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_bool__Orderings_Opreorder,axiom, % 0.60/0.72 class_Orderings_Opreorder(tc_bool) ). % 0.60/0.72 % 0.60/0.72 cnf(clsarity_bool__Orderings_Oorder,axiom, % 0.60/0.72 class_Orderings_Oorder(tc_bool) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom, % 0.60/0.72 hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ). % 0.60/0.72 % 0.60/0.72 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom, % 0.60/0.72 ( V_X = V_Y % 0.60/0.72 | ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ). % 0.60/0.72 % 0.60/0.72 %------------------------------------------------------------------------------ % 0.60/0.72 %------------------------------------------- % 0.60/0.72 % Proof found % 0.60/0.72 % SZS status Theorem for theBenchmark % 0.60/0.72 % SZS output start Proof % 0.60/0.72 %ClaNum:650(EqnAxiom:179) % 0.60/0.72 %VarNum:3019(SingletonVarNum:1191) % 0.60/0.72 %MaxLitNum:6 % 0.60/0.72 %MaxfuncDepth:7 % 0.60/0.72 %SharedTerms:87 % 0.60/0.72 %goalClause: 340 % 0.60/0.72 %singleGoalClaCount:1 % 0.60/0.72 [180]P1(a1) % 0.60/0.72 [181]P1(a2) % 0.60/0.72 [182]P2(a1) % 0.60/0.72 [183]P2(a2) % 0.60/0.72 [184]P24(a1) % 0.60/0.72 [185]P25(a1) % 0.60/0.72 [186]P3(a1) % 0.60/0.72 [187]P4(a1) % 0.60/0.72 [188]P5(a1) % 0.60/0.72 [189]P22(a1) % 0.60/0.72 [190]P6(a1) % 0.60/0.72 [191]P17(a1) % 0.60/0.72 [192]P26(a1) % 0.60/0.72 [193]P34(a1) % 0.60/0.72 [194]P28(a1) % 0.60/0.72 [195]P29(a1) % 0.60/0.72 [196]P27(a1) % 0.60/0.72 [197]P18(a1) % 0.60/0.72 [198]P19(a1) % 0.60/0.72 [199]P32(a1) % 0.60/0.72 [200]P21(a1) % 0.60/0.72 [201]P7(a1) % 0.60/0.72 [202]P8(a1) % 0.60/0.72 [203]P23(a1) % 0.60/0.72 [215]P9(a66,a61,a63) % 0.60/0.72 [216]P9(a68,a60,a63) % 0.60/0.72 [208]P35(f42(a5,a60)) % 0.60/0.72 [209]P35(f42(a5,a61)) % 0.60/0.72 [210]P35(f42(a5,a62)) % 0.60/0.72 [308]P9(f52(a66,a69,a63,a57),f37(a14,f42(f42(a14,f12(a70)),a62),a67,a55,a55),a64) % 0.60/0.72 [309]P9(f52(a68,a71,a63,a57),f37(a14,f42(f42(a14,f12(a70)),a62),a67,a55,a55),a65) % 0.60/0.72 [312]P35(f42(a5,f37(a14,f42(f42(f42(a20,a70),a62),f10(a1)),a67,a55,a55))) % 0.60/0.72 [340]~P35(f42(f42(a13,f37(a14,f42(f42(a14,f12(a70)),a62),a67,a55,a55)),f37(a14,f42(f42(f42(a20,a70),a62),f10(a1)),a67,a55,a55))) % 0.60/0.72 [324]~P11(x3241,x3241,a1) % 0.60/0.72 [328]~P11(x3281,f10(a1),a1) % 0.60/0.72 [205]E(f38(f3(x2051),x2051),f3(x2051)) % 0.60/0.72 [206]E(f41(f3(x2061),x2061),f3(x2061)) % 0.60/0.72 [207]E(f4(f3(x2071),x2071),f3(x2071)) % 0.60/0.72 [211]P35(f42(a5,f11(x2111))) % 0.60/0.72 [218]E(f42(f42(f6(a1),x2181),f10(a1)),x2181) % 0.60/0.72 [233]E(f47(f51(x2331),x2331,x2331),f51(x2331)) % 0.60/0.72 [294]E(f37(a14,f25(x2941),f26(x2941),a55,a55),x2941) % 0.60/0.72 [219]E(f42(f42(f6(a1),f10(a1)),x2191),x2191) % 0.60/0.72 [223]P10(x2231,f3(x2232),x2232) % 0.60/0.72 [236]P9(x2361,f11(x2362),f42(x2361,x2362)) % 0.60/0.72 [318]~E(f12(x3181),f11(x3182)) % 0.60/0.72 [214]E(f38(f38(x2141,x2142),x2142),x2141) % 0.60/0.72 [220]E(f43(f43(x2201,x2202),x2202),f43(x2201,x2202)) % 0.60/0.72 [222]E(f15(f10(a1),x2221,x2222),x2221) % 0.60/0.72 [227]E(f19(x2271,f3(x2272),x2272),x2271) % 0.60/0.72 [228]E(f19(f3(x2281),x2282,x2281),x2282) % 0.60/0.72 [230]E(f39(f10(a1),x2301,x2302),f3(x2302)) % 0.60/0.72 [231]E(f44(f10(a1),x2311,x2312),f3(x2312)) % 0.60/0.72 [232]E(f44(x2321,f3(x2322),x2322),f3(x2322)) % 0.60/0.72 [276]E(f42(f42(f42(a20,x2761),f15(f10(a1),x2762,f10(a1))),f10(a1)),f42(f42(f42(a20,x2761),x2762),f10(a1))) % 0.60/0.72 [237]E(f42(f42(f6(a1),x2371),x2372),f42(f42(f6(a1),x2372),x2371)) % 0.60/0.72 [238]P35(f42(f42(f51(x2381),x2382),x2382)) % 0.60/0.72 [241]E(f36(f35(x2411,f3(x2412),x2412),x2412),x2411) % 0.60/0.72 [242]E(f4(f35(x2421,f3(x2422),x2422),x2422),f3(x2422)) % 0.60/0.72 [243]E(f36(f19(x2431,f3(x2432),x2432),x2432),f36(x2431,x2432)) % 0.60/0.72 [244]E(f4(f19(x2441,f3(x2442),x2442),x2442),f4(x2441,x2442)) % 0.60/0.72 [251]E(f38(f35(x2511,f3(x2512),x2512),x2512),f35(x2511,f3(x2512),x2512)) % 0.60/0.72 [287]P35(f42(f42(a13,f42(f42(a14,f12(x2871)),x2872)),f42(f42(f42(a20,x2871),x2872),f10(a1)))) % 0.60/0.72 [333]~P35(f42(f42(a13,f11(x3331)),x3332)) % 0.60/0.72 [334]~P11(f42(f42(f6(a1),x3341),x3342),x3342,a1) % 0.60/0.72 [335]~P11(f42(f42(f6(a1),x3351),x3352),x3351,a1) % 0.60/0.72 [239]E(f42(f42(f42(a20,f11(x2391)),x2392),x2391),x2392) % 0.60/0.72 [260]E(f12(f42(f42(a16,x2601),f42(f42(f6(a1),x2602),f7(a1)))),f42(f42(a16,f12(x2601)),x2602)) % 0.60/0.72 [326]~E(f35(x3261,x3262,x3263),x3262) % 0.60/0.72 [331]~E(f35(x3311,x3312,x3313),f3(x3313)) % 0.60/0.72 [240]E(f39(f10(a1),x2401,x2402),f39(f10(a1),x2403,x2402)) % 0.60/0.72 [245]E(f47(f47(x2451,x2452,x2453),x2453,x2452),x2451) % 0.60/0.72 [247]E(f38(f39(x2471,x2472,x2473),x2473),f39(x2471,x2472,x2473)) % 0.60/0.72 [254]E(f44(f7(a1),f35(x2541,x2542,x2543),x2543),f35(x2541,f3(x2543),x2543)) % 0.60/0.72 [255]E(f19(f38(x2551,x2552),f38(x2553,x2552),x2552),f38(f19(x2553,x2551,x2552),x2552)) % 0.60/0.72 [257]E(f40(x2571,f3(x2572),x2572,x2573),f3(x2573)) % 0.60/0.72 [319]~E(f11(x3191),f42(f42(a14,x3192),x3193)) % 0.60/0.72 [320]~E(f12(x3201),f42(f42(a14,x3202),x3203)) % 0.60/0.72 [321]~E(f42(f42(a14,x3211),x3212),f11(x3213)) % 0.60/0.72 [322]~E(f42(f42(a14,x3221),x3222),f12(x3223)) % 0.60/0.72 [336]~P35(f42(f42(f28(x3361,x3362),x3363),f3(x3362))) % 0.60/0.72 [249]P35(f42(f42(f43(x2491,x2492),x2493),x2493)) % 0.60/0.72 [259]E(f19(x2591,f35(x2592,f3(x2593),x2593),x2593),f41(f35(x2592,x2591,x2593),x2593)) % 0.60/0.72 [261]E(f19(f38(x2611,x2612),f35(x2613,f3(x2612),x2612),x2612),f38(f35(x2613,x2611,x2612),x2612)) % 0.60/0.72 [279]E(f19(f39(x2791,x2792,x2793),f35(x2792,f3(x2793),x2793),x2793),f35(x2792,f39(x2791,x2792,x2793),x2793)) % 0.60/0.72 [315]E(f37(a14,f42(f42(a16,x3151),x3152),f40(f8(a16,x3152,a55,a1,a55),x3153,a55,a55),a55,a55),f42(f42(a16,f37(a14,x3151,x3153,a55,a55)),x3152)) % 0.60/0.72 [337]~P35(f42(f42(f28(x3371,x3372),f3(x3372)),x3373)) % 0.60/0.72 [258]E(f42(f42(f6(a1),x2581),f42(f42(f6(a1),x2582),x2583)),f42(f42(f6(a1),x2582),f42(f42(f6(a1),x2581),x2583))) % 0.60/0.72 [270]E(f36(f19(x2701,f35(x2702,f3(x2703),x2703),x2703),x2703),x2702) % 0.60/0.72 [271]E(f4(f19(x2711,f35(x2712,f3(x2713),x2713),x2713),x2713),x2711) % 0.60/0.72 [273]E(f12(f15(x2731,x2732,f42(f42(f6(a1),x2733),f7(a1)))),f15(x2731,f12(x2732),x2733)) % 0.60/0.72 [277]E(f42(f42(a14,f42(f42(a16,x2771),x2772)),f42(f42(a16,x2773),x2772)),f42(f42(a16,f42(f42(a14,x2771),x2773)),x2772)) % 0.60/0.72 [280]E(f38(f19(f38(x2801,x2802),f35(x2803,f3(x2802),x2802),x2802),x2802),f35(x2803,x2801,x2802)) % 0.60/0.72 [286]E(f12(f42(f42(f42(a20,x2861),f42(f42(a16,x2862),f10(a1))),f42(f42(f6(a1),x2863),f7(a1)))),f42(f42(f42(a20,f12(x2861)),x2862),x2863)) % 0.60/0.72 [304]E(f12(f42(f42(f42(a20,x3041),f15(f42(f42(f6(a1),x3042),f7(a1)),x3043,f10(a1))),f42(f42(f6(a1),x3042),f7(a1)))),f42(f42(f42(a20,f12(x3041)),f15(x3042,x3043,f10(a1))),x3042)) % 0.60/0.72 [313]E(f37(a14,x3131,f19(x3132,f35(x3133,f3(a55),a55),a55),a55,a55),f42(f42(a14,f37(a14,x3131,x3132,a55,a55)),x3133)) % 0.60/0.72 [272]E(f42(f42(f6(a1),f42(f42(f6(a1),x2721),x2722)),x2723),f42(f42(f6(a1),x2721),f42(f42(f6(a1),x2722),x2723))) % 0.60/0.72 [274]E(f42(f42(f42(a20,f42(f42(a16,x2741),x2742)),x2743),x2742),x2741) % 0.60/0.72 [267]E(f35(x2671,f19(x2672,x2673,x2674),x2674),f19(f35(x2671,x2672,x2674),x2673,x2674)) % 0.60/0.72 [269]E(f19(f19(x2691,x2692,x2693),x2694,x2693),f19(x2691,f19(x2692,x2694,x2693),x2693)) % 0.60/0.72 [282]E(f42(f52(x2821,x2822,x2823,x2824),x2822),x2823) % 0.60/0.72 [283]E(f19(f39(x2831,x2832,x2833),f39(x2834,x2832,x2833),x2833),f19(f39(x2834,x2832,x2833),f39(x2831,x2832,x2833),x2833)) % 0.60/0.72 [285]E(f38(f40(x2851,x2852,x2853,x2854),x2854),f40(x2851,f38(x2852,x2853),x2853,x2854)) % 0.60/0.72 [293]E(f37(x2931,x2932,f3(x2933),x2934,x2933),x2932) % 0.60/0.72 [339]~E(f37(a14,f12(x3391),x3392,a55,a55),f37(a14,f11(x3393),x3394,a55,a55)) % 0.60/0.72 [281]E(f42(f42(a14,f15(x2811,x2812,x2813)),f15(x2811,x2814,x2813)),f15(x2811,f42(f42(a14,x2812),x2814),x2813)) % 0.60/0.72 [284]E(f35(x2841,f19(f39(x2842,x2841,x2843),x2844,x2843),x2843),f19(f39(x2842,x2841,x2843),f35(x2841,x2844,x2843),x2843)) % 0.60/0.72 [338]~E(f42(f42(a14,f12(x3381)),x3382),f37(a14,f11(x3383),x3384,a55,a55)) % 0.60/0.72 [275]E(f19(f39(x2751,x2752,x2753),f39(x2754,x2752,x2753),x2753),f39(f42(f42(f6(a1),x2751),x2754),x2752,x2753)) % 0.60/0.72 [289]E(f42(f42(a14,f42(f42(f42(a20,x2891),x2892),x2893)),f42(f42(f42(a20,x2894),x2892),x2893)),f42(f42(f42(a20,f42(f42(a14,x2891),x2894)),x2892),x2893)) % 0.60/0.72 [316]E(f37(a14,f42(f42(f42(a20,x3161),x3162),x3163),f40(f8(f8(a20,x3162,a55,a55,f59(a1,a55)),x3163,a55,a1,a55),x3164,a55,a55),a55,a55),f42(f42(f42(a20,f37(a14,x3161,x3164,a55,a55)),x3162),x3163)) % 0.60/0.72 [278]E(f40(x2781,f39(x2782,x2783,x2784),x2784,x2785),f39(x2782,f42(x2781,x2783),x2785)) % 0.60/0.72 [288]E(f44(x2881,f40(x2882,x2883,x2884,x2885),x2885),f40(x2882,f44(x2881,x2883,x2884),x2884,x2885)) % 0.60/0.72 [291]E(f40(x2911,f35(x2912,x2913,x2914),x2914,x2915),f35(f42(x2911,x2912),f40(x2911,x2913,x2914,x2915),x2915)) % 0.60/0.72 [292]E(f35(f42(x2921,x2922),f40(x2921,x2923,x2924,x2925),x2925),f40(x2921,f35(x2922,x2923,x2924),x2924,x2925)) % 0.60/0.72 [298]E(f17(x2981,x2982,x2983,f11(x2984),x2985),f42(x2981,x2984)) % 0.60/0.72 [299]E(f17(x2991,x2992,x2993,f12(x2994),x2995),f42(x2993,x2994)) % 0.60/0.72 [300]E(f18(x3001,x3002,x3003,f11(x3004),x3005),f42(x3001,x3004)) % 0.60/0.72 [303]E(f19(f40(x3031,x3032,x3033,x3034),f40(x3031,x3035,x3033,x3034),x3034),f40(x3031,f19(x3032,x3035,x3033),x3033,x3034)) % 0.60/0.72 [310]E(f42(f42(x3101,x3102),f18(x3103,x3104,x3101,x3102,x3105)),f18(x3103,x3104,x3101,f12(x3102),x3105)) % 0.60/0.72 [305]E(f42(f8(x3051,x3052,x3053,x3054,x3055),x3056),f42(f42(x3051,x3056),x3052)) % 0.60/0.72 [311]E(f37(x3111,f37(x3111,x3112,x3113,x3114,x3115),x3116,x3114,x3115),f37(x3111,x3112,f19(x3113,x3116,x3115),x3114,x3115)) % 0.60/0.72 [302]E(f17(x3021,x3022,x3023,f42(f42(a14,x3024),x3025),x3026),f42(f42(x3022,x3024),x3025)) % 0.60/0.72 [307]E(f37(x3071,x3072,f35(x3073,x3074,x3075),x3076,x3075),f37(x3071,f42(f42(x3071,x3072),x3073),x3074,x3076,x3075)) % 0.60/0.72 [314]E(f42(f42(f42(f42(x3141,x3142),x3143),f18(x3144,x3141,x3145,x3142,x3146)),f18(x3144,x3141,x3145,x3143,x3146)),f18(x3144,x3141,x3145,f42(f42(a14,x3142),x3143),x3146)) % 0.60/0.72 [344]~P34(x3441)+~E(f7(x3441),f10(x3441)) % 0.60/0.72 [345]~P23(x3451)+P12(f6(x3451),x3451) % 0.60/0.72 [357]E(x3571,f10(a1))+P11(f10(a1),x3571,a1) % 0.60/0.72 [371]~P25(x3711)+P11(f10(x3711),f7(x3711),x3711) % 0.60/0.72 [404]~P25(x4041)+~P11(f7(x4041),f10(x4041),x4041) % 0.60/0.72 [346]~P24(x3461)+E(f48(f10(a1),x3461),f10(x3461)) % 0.60/0.72 [347]~P24(x3471)+E(f48(f7(a1),x3471),f7(x3471)) % 0.60/0.72 [376]~P20(x3761)+E(f42(f42(f6(x3761),f10(x3761)),f10(x3761)),f10(x3761)) % 0.60/0.72 [378]~P35(f42(a5,x3781))+P35(f42(a5,f12(x3781))) % 0.60/0.72 [455]~P25(x4551)+P11(f10(x4551),f42(f42(f6(x4551),f7(x4551)),f7(x4551)),x4551) % 0.60/0.72 [531]~P35(f42(a5,x5311))+P35(f42(f54(f47(a13,a55,a55),a55),x5311)) % 0.60/0.72 [549]P35(f42(a5,x5491))+~P35(f42(f54(f47(a13,a55,a55),a55),x5491)) % 0.60/0.72 [620]~P10(a5,x6201,a55)+P10(a5,f40(f8(a16,f10(a1),a55,a1,a55),x6201,a55,a55),a55) % 0.60/0.72 [384]~P11(x3842,x3842,x3841)+~P1(x3841) % 0.60/0.72 [385]~P11(x3852,x3852,x3851)+~P2(x3851) % 0.60/0.72 [386]~P11(x3862,x3862,x3861)+~P3(x3861) % 0.60/0.72 [341]E(x3411,x3412)+~E(f11(x3411),f11(x3412)) % 0.60/0.72 [342]E(x3421,x3422)+~E(f12(x3421),f12(x3422)) % 0.60/0.72 [349]~E(f38(x3491,x3492),f3(x3492))+E(x3491,f3(x3492)) % 0.60/0.72 [350]~E(f41(x3501,x3502),f3(x3502))+E(x3501,f3(x3502)) % 0.60/0.72 [351]~P1(x3512)+P1(f59(x3511,x3512)) % 0.60/0.72 [352]~P2(x3522)+P2(f59(x3521,x3522)) % 0.60/0.72 [420]~P25(x4201)+~P11(f48(x4202,x4201),f10(x4201),x4201) % 0.60/0.72 [358]~P26(x3582)+E(f49(x3581,f7(a1),x3582),x3581) % 0.60/0.72 [359]~P21(x3592)+E(f49(x3591,f7(a1),x3592),x3591) % 0.60/0.72 [360]~P26(x3601)+E(f42(f42(f6(x3601),x3602),f10(x3601)),x3602) % 0.60/0.72 [361]~P18(x3611)+E(f42(f42(f6(x3611),x3612),f10(x3611)),x3612) % 0.60/0.72 [362]~P19(x3621)+E(f42(f42(f6(x3621),x3622),f10(x3621)),x3622) % 0.60/0.72 [363]~P26(x3632)+E(f49(x3631,f10(a1),x3632),f7(x3632)) % 0.60/0.72 [364]~P27(x3642)+E(f49(x3641,f10(a1),x3642),f7(x3642)) % 0.60/0.72 [365]~P21(x3651)+E(f49(f7(x3651),x3652,x3651),f7(x3651)) % 0.60/0.72 [437]~P25(x4372)+P11(x4371,f42(f42(f6(x4372),x4371),f7(x4372)),x4372) % 0.60/0.72 [463]~P35(f42(f42(a13,x4631),x4632))+P35(f42(f42(a13,f12(x4631)),f12(x4632))) % 0.60/0.72 [603]~P24(x6031)+E(f50(f8(f6(x6031),f7(x6031),x6031,x6031,x6031),x6032,f10(x6031),x6031),f48(x6032,x6031)) % 0.60/0.72 [367]~P26(x3671)+E(f42(f42(f6(x3671),f10(x3671)),x3672),x3672) % 0.60/0.72 [368]~P18(x3681)+E(f42(f42(f6(x3681),f10(x3681)),x3682),x3682) % 0.60/0.72 [369]~P19(x3691)+E(f42(f42(f6(x3691),f10(x3691)),x3692),x3692) % 0.60/0.72 [373]E(x3731,f10(a1))+~E(f42(f42(f6(a1),x3732),x3731),x3732) % 0.60/0.72 [374]E(x3741,f10(a1))+~E(f42(f42(f6(a1),x3742),x3741),f10(a1)) % 0.60/0.72 [375]E(x3751,f10(a1))+~E(f42(f42(f6(a1),x3751),x3752),f10(a1)) % 0.60/0.72 [417]~P11(x4171,x4172,a1)+E(f42(f42(a16,f11(x4171)),x4172),f11(x4171)) % 0.60/0.72 [447]E(f12(f21(x4471,x4472)),x4472)+~P35(f42(f42(a13,f12(x4471)),x4472)) % 0.60/0.72 [452]P11(x4521,x4522,a1)+E(f42(f42(a16,f11(x4521)),x4522),f11(f42(f42(f6(a1),x4521),f7(a1)))) % 0.60/0.72 [457]~P35(f42(a5,x4571))+P35(f42(a5,f42(f42(a16,x4571),x4572))) % 0.60/0.72 [468]~P35(f42(a5,x4681))+P35(f42(a5,f42(f42(a14,x4681),f11(x4682)))) % 0.60/0.72 [470]E(x4701,f3(x4702))+E(f19(f4(x4701,x4702),f35(f36(x4701,x4702),f3(x4702),x4702),x4702),x4701) % 0.60/0.72 [480]P35(f42(f42(a13,x4801),f21(x4801,x4802)))+~P35(f42(f42(a13,f12(x4801)),x4802)) % 0.60/0.72 [523]P35(f42(f42(f43(a13,a55),f12(x5231)),f12(x5232)))+~P35(f42(f42(f43(a13,a55),x5231),x5232)) % 0.60/0.72 [619]~P10(a5,x6192,a55)+P35(f42(a5,f37(a14,f11(x6191),x6192,a55,a55))) % 0.60/0.72 [354]E(x3541,x3542)+~E(f38(x3541,x3543),f38(x3542,x3543)) % 0.60/0.72 [382]~E(f19(x3823,x3821,x3822),x3823)+E(x3821,f3(x3822)) % 0.60/0.72 [383]~E(f19(x3831,x3833,x3832),x3833)+E(x3831,f3(x3832)) % 0.60/0.72 [388]~E(f39(x3881,x3882,x3883),f3(x3883))+E(x3881,f10(a1)) % 0.60/0.72 [392]~E(f19(x3923,x3921,x3922),f3(x3922))+E(x3921,f3(x3922)) % 0.60/0.72 [393]~E(f19(x3931,x3933,x3932),f3(x3932))+E(x3931,f3(x3932)) % 0.60/0.72 [400]~P9(x4001,f11(x4002),x4003)+E(f42(x4001,x4002),x4003) % 0.60/0.72 [586]~E(f11(x5862),f37(a14,x5863,x5861,a55,a55))+E(x5861,f3(a55)) % 0.60/0.72 [587]~E(f12(x5872),f37(a14,x5873,x5871,a55,a55))+E(x5871,f3(a55)) % 0.60/0.72 [588]~E(f37(a14,x5882,x5881,a55,a55),f12(x5883))+E(x5881,f3(a55)) % 0.60/0.72 [590]E(x5901,f12(x5902))+~E(f37(a14,x5901,x5903,a55,a55),f12(x5902)) % 0.60/0.72 [591]E(f11(x5911),x5912)+~E(f11(x5911),f37(a14,x5912,x5913,a55,a55)) % 0.60/0.72 [592]E(f12(x5921),x5922)+~E(f12(x5921),f37(a14,x5922,x5923,a55,a55)) % 0.60/0.72 [612]E(x6121,x6122)+~E(f37(a14,x6121,x6123,a55,a55),f37(a14,x6122,x6123,a55,a55)) % 0.60/0.72 [412]E(x4121,f10(a1))+E(f36(f39(x4121,x4122,x4123),x4123),x4122) % 0.60/0.72 [418]E(x4181,f3(x4182))+E(f36(f35(x4183,x4181,x4182),x4182),f36(x4181,x4182)) % 0.60/0.72 [419]E(x4191,f3(x4192))+E(f36(f19(x4193,x4191,x4192),x4192),f36(x4191,x4192)) % 0.60/0.72 [424]~P11(x4242,x4243,a1)+E(f15(x4241,f11(x4242),x4243),f11(x4242)) % 0.60/0.72 [439]~E(f38(x4391,x4393),f35(x4392,f3(x4393),x4393))+E(x4391,f35(x4392,f3(x4393),x4393)) % 0.60/0.72 [440]~E(f35(x4402,f3(x4403),x4403),f38(x4401,x4403))+E(x4401,f35(x4402,f3(x4403),x4403)) % 0.60/0.72 [453]E(x4531,f3(x4532))+E(f35(x4533,f4(x4531,x4532),x4532),f4(f35(x4533,x4531,x4532),x4532)) % 0.60/0.72 [454]E(x4541,f3(x4542))+E(f19(x4543,f4(x4541,x4542),x4542),f4(f19(x4543,x4541,x4542),x4542)) % 0.60/0.72 [471]~P24(x4713)+E(f50(x4711,f10(a1),x4712,x4713),x4712) % 0.60/0.72 [593]E(f42(f42(a14,x5931),x5932),x5933)+~E(f42(f42(a14,x5931),x5932),f37(a14,x5933,f3(a55),a55,a55)) % 0.60/0.72 [631]~P35(f42(f42(a13,x6311),x6313))+P35(f42(f42(a13,f37(a14,x6311,x6312,a55,a55)),f37(a14,x6313,x6312,a55,a55))) % 0.60/0.72 [402]~P26(x4021)+E(f42(f42(f6(x4021),x4022),x4023),f42(f42(f6(x4021),x4023),x4022)) % 0.60/0.72 [403]~P18(x4031)+E(f42(f42(f6(x4031),x4032),x4033),f42(f42(f6(x4031),x4033),x4032)) % 0.60/0.72 [422]E(x4221,x4222)+~E(f42(f42(f6(a1),x4223),x4221),f42(f42(f6(a1),x4223),x4222)) % 0.60/0.72 [423]E(x4231,x4232)+~E(f42(f42(f6(a1),x4231),x4233),f42(f42(f6(a1),x4232),x4233)) % 0.60/0.72 [428]E(x4281,x4282)+~P35(f42(f42(f51(x4283),x4281),x4282)) % 0.60/0.72 [459]~P11(x4591,x4593,a1)+P11(x4591,f42(f42(f6(a1),x4592),x4593),a1) % 0.60/0.72 [461]~P11(x4611,x4612,a1)+P11(x4611,f42(f42(f6(a1),x4612),x4613),a1) % 0.60/0.72 [478]P11(x4781,x4782,a1)+~P11(f42(f42(f6(a1),x4781),x4783),x4782,a1) % 0.60/0.72 [488]~P11(x4881,x4883,a1)+P11(f42(f42(f6(a1),x4881),x4882),f42(f42(f6(a1),x4883),x4882),a1) % 0.60/0.72 [489]~P11(x4892,x4893,a1)+P11(f42(f42(f6(a1),x4891),x4892),f42(f42(f6(a1),x4891),x4893),a1) % 0.60/0.72 [495]~P10(f54(x4951,x4952),x4953,x4952)+P35(f42(f54(f28(x4951,x4952),f58(x4952)),x4953)) % 0.60/0.72 [514]P10(f54(x5141,x5142),x5143,x5142)+~P35(f42(f54(f28(x5141,x5142),f58(x5142)),x5143)) % 0.60/0.72 [520]P11(x5201,x5202,a1)+~P11(f42(f42(f6(a1),x5203),x5201),f42(f42(f6(a1),x5203),x5202),a1) % 0.60/0.72 [542]~P35(f42(f42(a13,x5421),x5423))+P35(f42(f42(a13,f42(f42(a14,x5421),x5422)),f42(f42(a14,x5423),x5422))) % 0.60/0.72 [543]~P35(f42(f42(a13,x5432),x5433))+P35(f42(f42(a13,f42(f42(a14,x5431),x5432)),f42(f42(a14,x5431),x5433))) % 0.60/0.72 [544]~P35(f42(f42(a13,x5441),x5443))+P35(f42(f42(a13,f42(f42(a16,x5441),x5442)),f42(f42(a16,x5443),x5442))) % 0.60/0.72 [551]~P35(f42(f42(f43(a13,a55),x5511),x5513))+P35(f42(f42(f43(a13,a55),f42(f42(a14,x5511),x5512)),f42(f42(a14,x5513),x5512))) % 0.60/0.72 [552]~P35(f42(f42(f43(a13,a55),x5522),x5523))+P35(f42(f42(f43(a13,a55),f42(f42(a14,x5521),x5522)),f42(f42(a14,x5521),x5523))) % 0.60/0.72 [553]~P35(f42(f42(f43(a13,a55),x5531),x5533))+P35(f42(f42(f43(a13,a55),f42(f42(a16,x5531),x5532)),f42(f42(a16,x5533),x5532))) % 0.60/0.72 [608]~P19(x6081)+E(f42(f42(f6(x6081),x6082),f37(f6(x6081),f10(x6081),x6083,x6081,x6081)),f37(f6(x6081),x6082,x6083,x6081,x6081)) % 0.60/0.72 [632]P35(f42(f42(a13,f37(a14,x6321,x6322,a55,a55)),f37(a14,x6321,x6323,a55,a55)))+~P35(f42(f42(f28(a13,a55),x6322),x6323)) % 0.60/0.72 [633]P35(f42(f42(f43(a13,a55),f37(a14,x6331,x6332,a55,a55)),f37(a14,x6333,x6332,a55,a55)))+~P35(f42(f42(f43(a13,a55),x6331),x6333)) % 0.60/0.72 [450]~P11(x4501,x4503,a1)+E(f42(f42(f42(a20,f11(x4501)),x4502),x4503),f11(x4501)) % 0.60/0.72 [456]P11(x4562,x4563,a1)+E(f15(x4561,f11(x4562),x4563),f11(f42(f42(f6(a1),x4562),x4561))) % 0.60/0.72 [469]~P24(x4691)+E(f42(f42(f6(x4691),f48(x4692,x4691)),f48(x4693,x4691)),f48(f42(f42(f6(a1),x4692),x4693),x4691)) % 0.60/0.72 [526]~P35(f42(a5,x5261))+P35(f42(a5,f42(f42(f42(a20,x5261),f11(x5262)),x5263))) % 0.60/0.72 [606]~E(f37(a14,f42(f42(a14,x6061),x6062),x6063,a55,a55),x6061)+E(f37(a14,f42(f42(a14,x6061),x6062),f19(x6063,f35(x6062,f3(a55),a55),a55),a55,a55),f42(f42(a14,x6061),x6062)) % 0.60/0.72 [634]P35(f42(f42(f28(a13,a55),x6341),f29(x6342,x6341,x6343)))+~P35(f42(f42(a13,f37(a14,f11(x6342),x6341,a55,a55)),x6343)) % 0.60/0.72 [639]E(f37(a14,f11(x6391),f29(x6391,x6392,x6393),a55,a55),x6393)+~P35(f42(f42(a13,f37(a14,f11(x6391),x6392,a55,a55)),x6393)) % 0.60/0.72 [353]E(x3531,x3532)+~E(f53(x3533,x3531),f53(x3534,x3532)) % 0.60/0.72 [355]E(x3551,x3552)+~E(f53(x3551,x3553),f53(x3552,x3554)) % 0.60/0.72 [430]E(x4301,x4302)+~E(f19(x4303,x4301,x4304),f19(x4303,x4302,x4304)) % 0.60/0.72 [432]E(x4321,x4322)+~E(f19(x4321,x4323,x4324),f19(x4322,x4323,x4324)) % 0.60/0.72 [482]P10(x4821,x4822,x4823)+~P10(x4821,f19(x4824,x4822,x4823),x4823) % 0.60/0.72 [483]P10(x4831,x4832,x4833)+~P10(x4831,f19(x4832,x4834,x4833),x4833) % 0.60/0.72 [512]~E(f40(x5123,x5121,x5122,x5124),f3(x5124))+E(x5121,f3(x5122)) % 0.60/0.72 [405]E(x4051,x4052)+~E(f42(f42(a14,x4053),x4051),f42(f42(a14,x4054),x4052)) % 0.60/0.72 [406]E(x4061,x4062)+~E(f42(f42(a14,x4061),x4063),f42(f42(a14,x4062),x4064)) % 0.60/0.72 [415]~P13(x4152,x4151,x4154)+E(f42(f42(x4151,x4152),x4153),x4153) % 0.60/0.72 [416]~P13(x4163,x4161,x4164)+E(f42(f42(x4161,x4162),x4163),x4162) % 0.60/0.72 [557]P9(x5571,f12(x5572),f53(x5573,x5574))+~P9(f52(x5571,f10(a1),x5573,a57),x5572,x5574) % 0.60/0.72 [614]E(x6141,x6142)+~E(f37(a14,f11(x6143),x6141,a55,a55),f37(a14,f11(x6144),x6142,a55,a55)) % 0.60/0.72 [615]E(x6151,x6152)+~E(f37(a14,f12(x6153),x6151,a55,a55),f37(a14,f12(x6154),x6152,a55,a55)) % 0.60/0.72 [616]E(x6161,x6162)+~E(f37(a14,f11(x6161),x6163,a55,a55),f37(a14,f11(x6162),x6164,a55,a55)) % 0.60/0.72 [617]E(x6171,x6172)+~E(f37(a14,f12(x6171),x6173,a55,a55),f37(a14,f12(x6172),x6174,a55,a55)) % 0.60/0.72 [481]~E(f38(x4811,x4813),f35(x4814,x4812,x4813))+E(x4811,f19(f38(x4812,x4813),f35(x4814,f3(x4813),x4813),x4813)) % 0.60/0.72 [484]~P35(f42(f42(x4841,x4843),x4844))+P35(f42(f42(f43(x4841,x4842),x4843),x4844)) % 0.60/0.72 [485]~P26(x4851)+E(f42(f42(f6(x4851),x4852),f42(f42(f6(x4851),x4853),x4854)),f42(f42(f6(x4851),x4853),f42(f42(f6(x4851),x4852),x4854))) % 0.60/0.72 [486]~P18(x4861)+E(f42(f42(f6(x4861),x4862),f42(f42(f6(x4861),x4863),x4864)),f42(f42(f6(x4861),x4863),f42(f42(f6(x4861),x4862),x4864))) % 0.60/0.72 [487]~P16(x4871)+E(f42(f42(f6(x4871),x4872),f42(f42(f6(x4871),x4873),x4874)),f42(f42(f6(x4871),x4873),f42(f42(f6(x4871),x4872),x4874))) % 0.60/0.72 [566]~P35(f42(f42(a13,x5661),x5664))+P35(f42(f42(a13,f42(f42(f42(a20,x5661),x5662),x5663)),f42(f42(f42(a20,x5664),x5662),x5663))) % 0.60/0.72 [570]~P35(f42(f42(a13,x5702),x5704))+P35(f42(f42(f43(a13,a55),f42(f42(f42(a20,x5701),x5702),x5703)),f42(f42(f42(a20,x5701),x5704),x5703))) % 0.60/0.72 [573]~P35(f42(f42(f43(x5731,x5732),x5734),x5733))+P35(f42(f42(f43(f47(x5731,x5732,x5732),x5732),x5733),x5734)) % 0.60/0.72 [577]~P35(f42(f42(f43(a13,a55),x5771),x5774))+P35(f42(f42(f43(a13,a55),f42(f42(f42(a20,x5771),x5772),x5773)),f42(f42(f42(a20,x5774),x5772),x5773))) % 0.60/0.72 [578]~P35(f42(f42(f43(a13,a55),x5782),x5784))+P35(f42(f42(f43(a13,a55),f42(f42(f42(a20,x5781),x5782),x5783)),f42(f42(f42(a20,x5781),x5784),x5783))) % 0.60/0.72 [585]P35(f42(f42(f43(x5851,x5852),x5853),x5854))+~P35(f42(f42(f43(f47(x5851,x5852,x5852),x5852),x5854),x5853)) % 0.60/0.72 [613]~P23(x6131)+E(f37(f6(x6131),f42(f42(f6(x6131),x6132),x6133),x6134,x6131,x6131),f42(f42(f6(x6131),x6132),f37(f6(x6131),x6133,x6134,x6131,x6131))) % 0.60/0.72 [517]~P26(x5171)+E(f42(f42(f6(x5171),f42(f42(f6(x5171),x5172),x5173)),x5174),f42(f42(f6(x5171),x5172),f42(f42(f6(x5171),x5173),x5174))) % 0.60/0.72 [518]~P18(x5181)+E(f42(f42(f6(x5181),f42(f42(f6(x5181),x5182),x5183)),x5184),f42(f42(f6(x5181),x5182),f42(f42(f6(x5181),x5183),x5184))) % 0.60/0.72 [519]~P7(x5191)+E(f42(f42(f6(x5191),f42(f42(f6(x5191),x5192),x5193)),x5194),f42(f42(f6(x5191),x5192),f42(f42(f6(x5191),x5193),x5194))) % 0.60/0.72 [533]~P26(x5331)+E(f42(f42(f6(x5331),f42(f42(f6(x5331),x5332),x5333)),x5334),f42(f42(f6(x5331),f42(f42(f6(x5331),x5332),x5334)),x5333)) % 0.60/0.72 [567]~P11(x5672,f42(f42(f6(a1),x5674),f7(a1)),a1)+E(f42(f42(f42(a20,f42(f42(a16,x5671),x5672)),f42(f42(a16,x5673),x5672)),f42(f42(f6(a1),x5674),f7(a1))),f42(f42(a16,f42(f42(f42(a20,x5671),x5673),x5674)),x5672)) % 0.60/0.72 [589]~P11(x5894,f42(f42(f6(a1),x5892),f7(a1)),a1)+E(f42(f42(f42(a20,f42(f42(a16,x5891),f42(f42(f6(a1),x5892),f7(a1)))),f42(f42(a16,x5893),x5892)),x5894),f42(f42(a16,f42(f42(f42(a20,x5891),x5893),x5894)),x5892)) % 0.60/0.72 [429]E(x4291,x4292)+~E(f35(x4293,x4291,x4294),f35(x4295,x4292,x4294)) % 0.60/0.72 [431]E(x4311,x4312)+~E(f35(x4311,x4313,x4314),f35(x4312,x4315,x4314)) % 0.60/0.72 [433]E(x4331,x4332)+~E(f39(x4331,x4333,x4334),f39(x4332,x4335,x4334)) % 0.60/0.72 [539]~P11(x5395,x5392,a1)+E(f42(f52(x5391,x5392,x5393,x5394),x5395),f42(x5391,x5395)) % 0.60/0.72 [547]~P9(x5471,x5474,x5475)+P9(f52(x5471,x5472,x5473,a57),f42(f42(a16,x5474),x5472),x5475) % 0.60/0.72 [558]~P35(f42(f42(x5581,x5583),x5585))+P35(f42(f42(f28(x5581,x5582),f35(x5583,x5584,x5582)),f35(x5585,x5584,x5582))) % 0.60/0.72 [610]~P13(x6103,x6101,x6105)+E(f42(f42(x6101,x6102),f37(x6101,x6103,x6104,x6105,x6105)),f37(x6101,x6102,x6104,x6105,x6105)) % 0.60/0.72 [621]~P15(x6211,x6214,x6215)+P15(f52(x6211,x6212,x6213,a57),f40(f8(a16,x6212,a55,a1,a55),x6214,a55,a55),x6215) % 0.60/0.72 [534]E(x5341,x5342)+~E(f19(x5343,f35(x5341,f3(x5344),x5344),x5344),f19(x5345,f35(x5342,f3(x5344),x5344),x5344)) % 0.60/0.72 [535]E(x5351,x5352)+~E(f19(x5351,f35(x5353,f3(x5354),x5354),x5354),f19(x5352,f35(x5355,f3(x5354),x5354),x5354)) % 0.60/0.72 [546]~P35(f42(f42(x5461,x5465),x5464))+P35(f42(f42(f47(x5461,x5462,x5463),x5464),x5465)) % 0.60/0.72 [555]P35(f42(f42(x5551,x5552),x5553))+~P35(f42(f42(f47(x5551,x5554,x5555),x5553),x5552)) % 0.60/0.72 [562]P35(f42(f42(f28(x5621,x5622),f35(x5623,x5624,x5622)),f35(x5623,x5625,x5622)))+~P35(f42(f42(f28(x5621,x5622),x5624),x5625)) % 0.60/0.72 [563]P35(f42(f42(f28(x5631,x5632),f19(x5633,x5634,x5632)),f19(x5635,x5634,x5632)))+~P35(f42(f42(f28(x5631,x5632),x5633),x5635)) % 0.60/0.72 [564]P35(f42(f42(f28(x5641,x5642),f19(x5643,x5644,x5642)),f19(x5643,x5645,x5642)))+~P35(f42(f42(f28(x5641,x5642),x5644),x5645)) % 0.60/0.72 [611]~P12(x6111,x6115)+E(f37(x6111,f42(f42(x6111,x6112),x6113),x6114,x6115,x6115),f42(f42(x6111,x6112),f37(x6111,x6113,x6114,x6115,x6115))) % 0.60/0.72 [624]P35(f42(x6241,f42(x6242,x6243)))+~P35(f42(x6241,f17(x6244,x6245,x6242,f12(x6243),a56))) % 0.60/0.72 [626]P35(f42(x6261,f42(x6262,x6263)))+~P35(f42(x6261,f17(x6262,x6264,x6265,f11(x6263),a56))) % 0.60/0.72 [494]~P12(x4941,x4945)+E(f42(f42(x4941,f42(f42(x4941,x4942),x4943)),x4944),f42(f42(x4941,x4942),f42(f42(x4941,x4943),x4944))) % 0.60/0.72 [548]~P26(x5481)+E(f42(f42(f6(x5481),f42(f42(f6(x5481),x5482),x5483)),f42(f42(f6(x5481),x5484),x5485)),f42(f42(f6(x5481),f42(f42(f6(x5481),x5482),x5484)),f42(f42(f6(x5481),x5483),x5485))) % 0.60/0.72 [629]P35(f42(x6291,f42(f42(x6292,x6293),x6294)))+~P35(f42(x6291,f17(x6295,x6292,x6296,f42(f42(a14,x6293),x6294),a56))) % 0.60/0.72 [399]E(x3991,x3992)+P11(x3992,x3991,a1)+P11(x3991,x3992,a1) % 0.60/0.72 [446]~P25(x4461)+P11(f10(x4461),f48(x4462,x4461),x4461)+~P11(f10(a1),x4462,a1) % 0.60/0.72 [451]~P25(x4512)+~P11(f10(x4512),f48(x4511,x4512),x4512)+P11(f10(a1),x4511,a1) % 0.60/0.72 [370]~P30(x3701)+~P14(x3701)+E(f42(f42(f6(x3701),x3702),f10(x3701)),x3702) % 0.60/0.72 [425]P11(f9(x4251,x4252),x4252,a1)+~P35(f42(x4251,x4252))+P35(f42(x4251,f10(a1))) % 0.60/0.72 [394]~P20(x3942)+E(x3941,f10(x3942))+~E(f42(f42(f6(x3942),x3941),x3941),f10(x3942)) % 0.60/0.72 [473]~P20(x4731)+~P11(f10(x4731),x4732,x4731)+P11(f10(x4731),f42(f42(f6(x4731),x4732),x4732),x4731) % 0.60/0.72 [474]~P31(x4741)+~P11(x4742,f10(x4741),x4741)+P11(f42(f42(f6(x4741),x4742),x4742),f10(x4741),x4741) % 0.60/0.72 [475]~P20(x4751)+~P11(x4752,f10(x4751),x4751)+P11(f42(f42(f6(x4751),x4752),x4752),f10(x4751),x4751) % 0.60/0.72 [490]~P31(x4902)+P11(x4901,f10(x4902),x4902)+~P11(f42(f42(f6(x4902),x4901),x4901),f10(x4902),x4902) % 0.60/0.72 [491]~P20(x4912)+P11(x4911,f10(x4912),x4912)+~P11(f42(f42(f6(x4912),x4911),x4911),f10(x4912),x4912) % 0.60/0.72 [492]~P20(x4921)+P11(f10(x4921),x4922,x4921)+~P11(f10(x4921),f42(f42(f6(x4921),x4922),x4922),x4921) % 0.60/0.72 [499]P11(f10(a1),x4991,a1)+P11(f10(a1),x4992,a1)+~P11(f10(a1),f42(f42(f6(a1),x4991),x4992),a1) % 0.60/0.72 [532]~P35(f42(x5321,x5322))+P35(f42(x5321,f10(a1)))+P35(f42(x5321,f42(f42(f6(a1),f9(x5321,x5322)),f7(a1)))) % 0.60/0.72 [442]~P11(x4423,x4422,x4421)+~P1(x4421)+~P11(x4422,x4423,x4421) % 0.60/0.72 [443]~P11(x4433,x4432,x4431)+~P2(x4431)+~P11(x4432,x4433,x4431) % 0.60/0.72 [444]~P11(x4443,x4442,x4441)+~P3(x4441)+~P11(x4442,x4443,x4441) % 0.60/0.72 [356]~P8(x3563)+E(x3561,x3562)+~E(f48(x3561,x3563),f48(x3562,x3563)) % 0.60/0.72 [395]~E(f44(x3953,x3951,x3952),f3(x3952))+E(x3951,f3(x3952))+E(x3953,f10(a1)) % 0.60/0.72 [397]~P33(x3972)+~E(f49(x3971,x3973,x3972),f10(x3972))+E(x3971,f10(x3972)) % 0.60/0.72 [449]~P25(x4492)+~P11(x4491,x4493,a1)+P11(f48(x4491,x4492),f48(x4493,x4492),x4492) % 0.60/0.72 [462]~P25(x4623)+~P11(f48(x4621,x4623),f48(x4622,x4623),x4623)+P11(x4621,x4622,a1) % 0.60/0.72 [476]~P25(x4761)+~P11(f10(x4761),x4762,x4761)+P11(f10(x4761),f49(x4762,x4763,x4761),x4761) % 0.60/0.72 [427]E(x4271,x4272)+P11(x4272,x4271,a1)+E(f42(f42(f42(a20,f11(x4271)),x4273),x4272),f11(x4271)) % 0.60/0.72 [630]~P35(f42(a5,x6302))+~P35(f42(a5,f37(a14,f42(f42(f42(a20,x6301),x6302),f10(a1)),x6303,a55,a55)))+P35(f42(a5,f37(a14,f42(f42(a14,f12(x6301)),x6302),x6303,a55,a55))) % 0.60/0.72 [635]~P35(f42(f54(f47(a13,a55,a55),a55),x6352))+~P35(f42(f54(f47(a13,a55,a55),a55),f37(a14,f42(f42(f42(a20,x6351),x6352),f10(a1)),x6353,a55,a55)))+P35(f42(f54(f47(a13,a55,a55),a55),f37(a14,f42(f42(a14,f12(x6351)),x6352),x6353,a55,a55))) % 0.60/0.72 [493]~P10(x4931,x4933,x4934)+~P10(x4931,x4932,x4934)+P10(x4931,f19(x4932,x4933,x4934),x4934) % 0.60/0.72 [472]P9(x4721,x4722,x4723)+~P9(x4721,x4724,x4723)+~P35(f42(f42(a13,x4724),x4722)) % 0.60/0.72 [498]~P35(f42(f54(x4981,x4982),x4984))+P35(f42(f54(x4981,x4982),x4983))+~P35(f42(f42(x4981,x4983),x4984)) % 0.60/0.72 [607]E(x6071,f3(a55))+E(f37(a14,x6072,f27(x6073,x6074,x6072,x6071),a55,a55),x6073)+~E(f42(f42(a14,x6073),x6074),f37(a14,x6072,x6071,a55,a55)) % 0.60/0.72 [434]~P6(x4343)+E(x4341,x4342)+~E(f42(f42(f6(x4343),x4344),x4341),f42(f42(f6(x4343),x4344),x4342)) % 0.60/0.72 [435]~P17(x4353)+E(x4351,x4352)+~E(f42(f42(f6(x4353),x4354),x4351),f42(f42(f6(x4353),x4354),x4352)) % 0.60/0.72 [436]~P17(x4363)+E(x4361,x4362)+~E(f42(f42(f6(x4363),x4361),x4364),f42(f42(f6(x4363),x4362),x4364)) % 0.60/0.72 [479]~P11(x4794,x4793,a1)+P11(x4791,x4792,a1)+~E(f42(f42(f6(a1),x4791),x4793),f42(f42(f6(a1),x4794),x4792)) % 0.60/0.72 [501]~P4(x5011)+~P11(x5012,x5014,x5011)+P11(f42(f42(f6(x5011),x5012),x5013),f42(f42(f6(x5011),x5014),x5013),x5011) % 0.60/0.72 [502]~P5(x5021)+~P11(x5022,x5024,x5021)+P11(f42(f42(f6(x5021),x5022),x5023),f42(f42(f6(x5021),x5024),x5023),x5021) % 0.60/0.72 [503]~P4(x5031)+~P11(x5033,x5034,x5031)+P11(f42(f42(f6(x5031),x5032),x5033),f42(f42(f6(x5031),x5032),x5034),x5031) % 0.60/0.72 [504]~P5(x5041)+~P11(x5043,x5044,x5041)+P11(f42(f42(f6(x5041),x5042),x5043),f42(f42(f6(x5041),x5042),x5044),x5041) % 0.60/0.72 [509]P9(x5091,x5092,x5093)+~P9(x5091,x5094,x5093)+~P35(f42(f42(f43(a13,a55),x5094),x5092)) % 0.60/0.72 [513]~P11(x5132,x5134,a1)+~P11(x5131,x5133,a1)+P11(f42(f42(f6(a1),x5131),x5132),f42(f42(f6(a1),x5133),x5134),a1) % 0.60/0.72 [527]~P5(x5273)+P11(x5271,x5272,x5273)+~P11(f42(f42(f6(x5273),x5274),x5271),f42(f42(f6(x5273),x5274),x5272),x5273) % 0.60/0.72 [528]~P5(x5283)+P11(x5281,x5282,x5283)+~P11(f42(f42(f6(x5283),x5281),x5284),f42(f42(f6(x5283),x5282),x5284),x5283) % 0.60/0.72 [530]P35(f42(f54(x5301,x5302),x5303))+~P35(f42(f54(x5301,x5302),x5304))+~P35(f42(f42(f43(x5301,x5302),x5303),x5304)) % 0.60/0.72 [556]~P35(f42(f54(x5561,x5562),x5563))+P35(f42(f54(f28(x5561,x5562),f58(x5562)),f35(x5563,x5564,x5562)))+~P35(f42(f54(f28(x5561,x5562),f58(x5562)),x5564)) % 0.60/0.72 [560]~P35(f42(f42(f43(a13,a55),x5601),x5603))+~P35(f42(f42(f43(a13,a55),x5602),x5604))+P35(f42(f42(f43(a13,a55),f42(f42(a14,x5601),x5602)),f42(f42(a14,x5603),x5604))) % 0.60/0.72 [594]E(x5941,f3(a55))+~E(f42(f42(a14,x5942),x5943),f37(a14,x5944,x5941,a55,a55))+E(f19(f27(x5942,x5943,x5944,x5941),f35(x5943,f3(a55),a55),a55),x5941) % 0.60/0.72 [438]E(x4381,x4382)+~E(f39(x4383,x4381,x4384),f39(x4385,x4382,x4384))+E(x4383,f10(a1)) % 0.60/0.72 [496]~P9(x4961,x4963,x4965)+~P9(x4961,x4962,f53(x4965,x4964))+P9(x4961,f42(f42(a14,x4962),x4963),x4964) % 0.60/0.72 [595]~E(f19(x5951,x5955,x5952),f35(x5953,x5954,x5952))+E(x5951,f3(x5952))+E(f35(x5953,f45(x5953,x5954,x5951,x5955,x5952),x5952),x5951) % 0.60/0.72 [596]~E(f19(x5961,x5965,x5962),f35(x5963,x5964,x5962))+E(x5961,f3(x5962))+E(f19(f46(x5963,x5964,x5961,x5965,x5962),x5965,x5962),x5964) % 0.60/0.72 [597]~E(f19(x5971,x5975,x5972),f35(x5973,x5974,x5972))+E(x5971,f3(x5972))+E(f35(x5973,f46(x5973,x5974,x5971,x5975,x5972),x5972),x5971) % 0.60/0.72 [598]~E(f19(x5981,x5985,x5982),f35(x5983,x5984,x5982))+E(x5981,f3(x5982))+E(f19(f45(x5983,x5984,x5981,x5985,x5982),x5985,x5982),x5984) % 0.60/0.72 [599]~E(f19(x5995,x5991,x5994),f35(x5992,x5993,x5994))+E(x5991,f35(x5992,x5993,x5994))+E(f35(x5992,f45(x5992,x5993,x5995,x5991,x5994),x5994),x5995) % 0.60/0.72 [600]~E(f19(x6005,x6001,x6004),f35(x6002,x6003,x6004))+E(x6001,f35(x6002,x6003,x6004))+E(f19(f45(x6002,x6003,x6005,x6001,x6004),x6001,x6004),x6003) % 0.60/0.72 [601]~E(f19(x6015,x6014,x6013),f35(x6011,x6012,x6013))+E(f35(x6011,x6012,x6013),x6014)+E(f19(f46(x6011,x6012,x6015,x6014,x6013),x6014,x6013),x6012) % 0.60/0.72 [602]~E(f19(x6025,x6024,x6023),f35(x6021,x6022,x6023))+E(f35(x6021,x6022,x6023),x6024)+E(f35(x6021,f46(x6021,x6022,x6025,x6024,x6023),x6023),x6025) % 0.60/0.72 [627]E(x6271,x6272)+~P9(x6273,f37(a14,f11(x6274),x6275,a55,a55),x6271)+~P9(x6273,f37(a14,f11(x6274),x6275,a55,a55),x6272) % 0.60/0.72 [540]~P35(f42(f42(x5401,x5405),x5404))+~P35(f42(f42(f43(x5401,x5402),x5403),x5405))+P35(f42(f42(f43(x5401,x5402),x5403),x5404)) % 0.60/0.72 [541]~P35(f42(f42(x5411,x5413),x5415))+~P35(f42(f42(f43(x5411,x5412),x5415),x5414))+P35(f42(f42(f43(x5411,x5412),x5413),x5414)) % 0.60/0.72 [550]~P35(f42(f42(f43(x5501,x5502),x5503),x5505))+P35(f42(f42(f43(x5501,x5502),x5503),x5504))+~P35(f42(f42(f43(x5501,x5502),x5505),x5504)) % 0.60/0.72 [508]~P16(x5081)+E(f42(f42(f6(x5081),x5082),x5083),x5084)+~E(f42(f42(f6(x5081),x5082),f42(f42(f6(x5081),x5085),x5083)),f42(f42(f6(x5081),x5085),x5084)) % 0.60/0.72 [571]E(x5711,x5712)+E(x5713,x5714)+~P35(f42(f42(f28(x5715,x5716),f35(x5714,x5712,x5716)),f35(x5713,x5711,x5716))) % 0.60/0.72 [574]E(x5741,x5742)+~P35(f42(f42(f28(x5743,x5744),f35(x5742,x5745,x5744)),f35(x5741,x5746,x5744)))+P35(f42(f42(x5743,x5742),x5741)) % 0.60/0.72 [565]~P9(x5651,x5653,x5656)+~P9(f52(x5651,x5654,x5656,a57),x5652,x5655)+P9(x5651,f42(f42(f42(a20,x5652),x5653),x5654),x5655) % 0.60/0.72 [580]E(x5801,x5802)+~P35(f42(f42(f28(x5803,x5804),f35(x5805,x5801,x5804)),f35(x5806,x5802,x5804)))+P35(f42(f42(f28(x5803,x5804),x5801),x5802)) % 0.60/0.72 [582]~P35(f42(f42(f28(x5821,x5824),f35(x5822,x5825,x5824)),f35(x5823,x5826,x5824)))+P35(f42(f42(x5821,x5822),x5823))+P35(f42(f42(f28(x5821,x5824),x5825),x5826)) % 0.60/0.72 [604]E(x6041,x6042)+E(x6043,x6044)+~P35(f42(f42(f28(x6045,x6046),f19(x6043,f35(x6041,f3(x6046),x6046),x6046)),f19(x6044,f35(x6042,f3(x6046),x6046),x6046))) % 0.60/0.72 [605]E(x6051,x6052)+P35(f42(f42(x6053,x6051),x6052))+~P35(f42(f42(f28(x6053,x6054),f19(x6055,f35(x6051,f3(x6054),x6054),x6054)),f19(x6056,f35(x6052,f3(x6054),x6054),x6054))) % 0.60/0.72 [609]E(x6091,x6092)+P35(f42(f42(f28(x6093,x6094),x6091),x6092))+~P35(f42(f42(f28(x6093,x6094),f19(x6091,f35(x6095,f3(x6094),x6094),x6094)),f19(x6092,f35(x6096,f3(x6094),x6094),x6094))) % 0.60/0.72 [618]P35(f42(f42(x6181,x6182),x6183))+P35(f42(f42(f28(x6181,x6184),x6185),x6186))+~P35(f42(f42(f28(x6181,x6184),f19(x6185,f35(x6182,f3(x6184),x6184),x6184)),f19(x6186,f35(x6183,f3(x6184),x6184),x6184))) % 0.60/0.72 [637]~P9(x6371,x6372,x6376)+~P15(f52(x6371,x6373,x6376,a57),x6374,x6375)+P15(x6371,f40(f8(f8(a20,x6372,a55,a55,f59(a1,a55)),x6373,a55,a1,a55),x6374,a55,a55),x6375) % 0.60/0.72 [379]~P27(x3792)+~P32(x3792)+E(x3791,f10(a1))+E(f49(f10(x3792),x3791,x3792),f10(x3792)) % 0.60/0.72 [410]P11(x4101,x4102,x4103)+~P3(x4103)+E(x4101,x4102)+P11(x4102,x4101,x4103) % 0.60/0.72 [411]P11(x4111,x4112,x4113)+~P31(x4113)+E(x4111,x4112)+P11(x4112,x4111,x4113) % 0.60/0.72 [505]~P25(x5051)+~P11(f7(x5051),x5052,x5051)+P11(f7(x5051),f49(x5052,x5053,x5051),x5051)+~P11(f10(a1),x5053,a1) % 0.60/0.72 [396]~P30(x3962)+~P14(x3962)+E(x3961,f10(x3962))+~E(f42(f42(f6(x3962),x3963),x3961),x3963) % 0.60/0.72 [506]~P22(x5061)+~P11(f10(x5061),x5063,x5061)+~P11(f10(x5061),x5062,x5061)+P11(f10(x5061),f42(f42(f6(x5061),x5062),x5063),x5061) % 0.60/0.72 [507]~P22(x5071)+~P11(x5073,f10(x5071),x5071)+~P11(x5072,f10(x5071),x5071)+P11(f42(f42(f6(x5071),x5072),x5073),f10(x5071),x5071) % 0.60/0.72 [636]E(f12(f30(x6361,x6362,x6363)),x6361)+P35(f42(f42(f28(a13,a55),x6362),f32(x6361,x6362,x6363)))+P35(f42(f42(a13,x6361),f31(x6361,x6362,x6363)))+~P35(f42(f42(a13,f37(a14,x6361,x6362,a55,a55)),x6363)) % 0.60/0.72 [638]E(f35(f33(x6381,x6382,x6383),f34(x6381,x6382,x6383),a55),x6382)+P35(f42(f42(f28(a13,a55),x6382),f32(x6381,x6382,x6383)))+P35(f42(f42(a13,x6381),f31(x6381,x6382,x6383)))+~P35(f42(f42(a13,f37(a14,x6381,x6382,a55,a55)),x6383)) % 0.60/0.72 [640]E(f12(f30(x6401,x6402,x6403)),x6401)+E(f37(a14,x6401,f32(x6401,x6402,x6403),a55,a55),x6403)+P35(f42(f42(a13,x6401),f31(x6401,x6402,x6403)))+~P35(f42(f42(a13,f37(a14,x6401,x6402,a55,a55)),x6403)) % 0.60/0.72 [641]E(f12(f30(x6411,x6412,x6413)),x6411)+E(f37(a14,f31(x6411,x6412,x6413),x6412,a55,a55),x6413)+P35(f42(f42(f28(a13,a55),x6412),f32(x6411,x6412,x6413)))+~P35(f42(f42(a13,f37(a14,x6411,x6412,a55,a55)),x6413)) % 0.60/0.72 [642]E(f35(f33(x6421,x6422,x6423),f34(x6421,x6422,x6423),a55),x6422)+E(f37(a14,x6421,f32(x6421,x6422,x6423),a55,a55),x6423)+P35(f42(f42(a13,x6421),f31(x6421,x6422,x6423)))+~P35(f42(f42(a13,f37(a14,x6421,x6422,a55,a55)),x6423)) % 0.60/0.72 [643]E(f35(f33(x6431,x6432,x6433),f34(x6431,x6432,x6433),a55),x6432)+E(f37(a14,f31(x6431,x6432,x6433),x6432,a55,a55),x6433)+P35(f42(f42(f28(a13,a55),x6432),f32(x6431,x6432,x6433)))+~P35(f42(f42(a13,f37(a14,x6431,x6432,a55,a55)),x6433)) % 0.60/0.72 [644]E(f12(f30(x6441,x6442,x6443)),x6441)+E(f37(a14,x6441,f32(x6441,x6442,x6443),a55,a55),x6443)+E(f37(a14,f31(x6441,x6442,x6443),x6442,a55,a55),x6443)+~P35(f42(f42(a13,f37(a14,x6441,x6442,a55,a55)),x6443)) % 0.60/0.72 [645]E(f35(f33(x6451,x6452,x6453),f34(x6451,x6452,x6453),a55),x6452)+E(f37(a14,x6451,f32(x6451,x6452,x6453),a55,a55),x6453)+E(f37(a14,f31(x6451,x6452,x6453),x6452,a55,a55),x6453)+~P35(f42(f42(a13,f37(a14,x6451,x6452,a55,a55)),x6453)) % 0.60/0.72 [646]E(f37(a14,f42(f42(f42(a20,f30(x6461,x6462,x6463)),f33(x6461,x6462,x6463)),f10(a1)),f34(x6461,x6462,x6463),a55,a55),x6463)+P35(f42(f42(f28(a13,a55),x6462),f32(x6461,x6462,x6463)))+P35(f42(f42(a13,x6461),f31(x6461,x6462,x6463)))+~P35(f42(f42(a13,f37(a14,x6461,x6462,a55,a55)),x6463)) % 0.60/0.72 [647]E(f37(a14,x6471,f32(x6471,x6472,x6473),a55,a55),x6473)+E(f37(a14,f42(f42(f42(a20,f30(x6471,x6472,x6473)),f33(x6471,x6472,x6473)),f10(a1)),f34(x6471,x6472,x6473),a55,a55),x6473)+P35(f42(f42(a13,x6471),f31(x6471,x6472,x6473)))+~P35(f42(f42(a13,f37(a14,x6471,x6472,a55,a55)),x6473)) % 0.60/0.72 [648]E(f37(a14,f31(x6481,x6482,x6483),x6482,a55,a55),x6483)+E(f37(a14,f42(f42(f42(a20,f30(x6481,x6482,x6483)),f33(x6481,x6482,x6483)),f10(a1)),f34(x6481,x6482,x6483),a55,a55),x6483)+P35(f42(f42(f28(a13,a55),x6482),f32(x6481,x6482,x6483)))+~P35(f42(f42(a13,f37(a14,x6481,x6482,a55,a55)),x6483)) % 0.60/0.72 [649]E(f37(a14,f31(x6491,x6492,x6493),x6492,a55,a55),x6493)+E(f37(a14,x6491,f32(x6491,x6492,x6493),a55,a55),x6493)+E(f37(a14,f42(f42(f42(a20,f30(x6491,x6492,x6493)),f33(x6491,x6492,x6493)),f10(a1)),f34(x6491,x6492,x6493),a55,a55),x6493)+~P35(f42(f42(a13,f37(a14,x6491,x6492,a55,a55)),x6493)) % 0.60/0.72 [559]E(f12(f22(x5591,x5592,x5593)),x5591)+E(f42(f42(a14,x5591),f23(x5591,x5592,x5593)),x5593)+E(f42(f42(a14,f24(x5591,x5592,x5593)),x5592),x5593)+~P35(f42(f42(a13,f42(f42(a14,x5591),x5592)),x5593)) % 0.60/0.72 [561]E(f12(f22(x5611,x5612,x5613)),x5611)+E(f42(f42(a14,x5611),f23(x5611,x5612,x5613)),x5613)+P35(f42(f42(a13,x5611),f24(x5611,x5612,x5613)))+~P35(f42(f42(a13,f42(f42(a14,x5611),x5612)),x5613)) % 0.60/0.72 [568]E(f12(f22(x5681,x5682,x5683)),x5681)+E(f42(f42(a14,f24(x5681,x5682,x5683)),x5682),x5683)+P35(f42(f42(a13,x5682),f23(x5681,x5682,x5683)))+~P35(f42(f42(a13,f42(f42(a14,x5681),x5682)),x5683)) % 0.60/0.72 [569]E(f12(f22(x5691,x5692,x5693)),x5691)+P35(f42(f42(a13,x5691),f24(x5691,x5692,x5693)))+P35(f42(f42(a13,x5692),f23(x5691,x5692,x5693)))+~P35(f42(f42(a13,f42(f42(a14,x5691),x5692)),x5693)) % 0.60/0.72 [579]E(f42(f42(a14,x5791),f23(x5791,x5792,x5793)),x5793)+E(f42(f42(f42(a20,f22(x5791,x5792,x5793)),x5792),f10(a1)),x5793)+E(f42(f42(a14,f24(x5791,x5792,x5793)),x5792),x5793)+~P35(f42(f42(a13,f42(f42(a14,x5791),x5792)),x5793)) % 0.60/0.72 [581]E(f42(f42(a14,x5811),f23(x5811,x5812,x5813)),x5813)+E(f42(f42(f42(a20,f22(x5811,x5812,x5813)),x5812),f10(a1)),x5813)+P35(f42(f42(a13,x5811),f24(x5811,x5812,x5813)))+~P35(f42(f42(a13,f42(f42(a14,x5811),x5812)),x5813)) % 0.60/0.72 [583]E(f42(f42(f42(a20,f22(x5831,x5832,x5833)),x5832),f10(a1)),x5833)+E(f42(f42(a14,f24(x5831,x5832,x5833)),x5832),x5833)+P35(f42(f42(a13,x5832),f23(x5831,x5832,x5833)))+~P35(f42(f42(a13,f42(f42(a14,x5831),x5832)),x5833)) % 0.60/0.72 [584]E(f42(f42(f42(a20,f22(x5841,x5842,x5843)),x5842),f10(a1)),x5843)+P35(f42(f42(a13,x5841),f24(x5841,x5842,x5843)))+P35(f42(f42(a13,x5842),f23(x5841,x5842,x5843)))+~P35(f42(f42(a13,f42(f42(a14,x5841),x5842)),x5843)) % 0.60/0.72 [464]~P1(x4643)+~P11(x4641,x4644,x4643)+P11(x4641,x4642,x4643)+~P11(x4644,x4642,x4643) % 0.60/0.72 [465]~P2(x4653)+~P11(x4651,x4654,x4653)+P11(x4651,x4652,x4653)+~P11(x4654,x4652,x4653) % 0.60/0.72 [477]~P25(x4774)+E(x4771,x4772)+~P11(f7(x4774),x4773,x4774)+~E(f49(x4773,x4771,x4774),f49(x4773,x4772,x4774)) % 0.60/0.72 [525]~P25(x5253)+~P11(x5252,x5254,a1)+~P11(f7(x5253),x5251,x5253)+P11(f49(x5251,x5252,x5253),f49(x5251,x5254,x5253),x5253) % 0.60/0.72 [538]~P25(x5383)+~P11(f49(x5384,x5381,x5383),f49(x5384,x5382,x5383),x5383)+P11(x5381,x5382,a1)+~P11(f7(x5383),x5384,x5383) % 0.60/0.72 [445]~P30(x4453)+~P14(x4453)+E(x4451,x4452)+~E(f42(f42(f6(x4453),x4454),x4451),f42(f42(f6(x4453),x4454),x4452)) % 0.60/0.72 [500]~P25(x5002)+~P11(x5001,x5004,x5002)+~P11(f10(x5002),x5003,x5002)+P11(x5001,f42(f42(f6(x5002),x5003),x5004),x5002) % 0.60/0.72 [572]~P9(x5723,x5721,a63)+~P9(f52(x5723,x5722,a63,a57),a62,x5724)+~P35(f42(a5,x5721))+P35(f42(a5,f42(f42(f42(a20,a62),x5721),x5722))) % 0.60/0.72 [650]~P9(x6503,x6501,a63)+~P9(f52(x6503,x6502,a63,a57),f37(a14,f42(f42(f42(a20,a70),a62),f10(a1)),a67,a55,a55),x6504)+~P35(f42(a5,x6501))+P35(f42(a5,f42(f42(f42(a20,f37(a14,f42(f42(f42(a20,a70),a62),f10(a1)),a67,a55,a55)),x6501),x6502))) % 0.60/0.72 [521]~P4(x5211)+~P11(x5213,x5215,x5211)+~P11(x5212,x5214,x5211)+P11(f42(f42(f6(x5211),x5212),x5213),f42(f42(f6(x5211),x5214),x5215),x5211) % 0.60/0.72 [413]~P34(x4132)+~P28(x4132)+~P29(x4132)+~P27(x4132)+~E(f49(x4131,f10(a1),x4132),f10(x4132)) % 0.60/0.72 [536]~P25(x5363)+~P11(x5364,x5362,a1)+~P11(x5361,f7(x5363),x5363)+~P11(f10(x5363),x5361,x5363)+P11(f49(x5361,x5362,x5363),f49(x5361,x5364,x5363),x5363) % 0.60/0.72 [389]~P34(x3892)+~P28(x3892)+~P29(x3892)+~P27(x3892)+E(x3891,f10(a1))+E(f49(f10(x3892),x3891,x3892),f10(x3892)) % 0.60/0.72 [414]~P34(x4142)+~P28(x4142)+~P29(x4142)+~P27(x4142)+~E(f49(x4141,x4143,x4142),f10(x4142))+E(x4141,f10(x4142)) % 0.60/0.72 [575]~P9(x5756,x5752,x5755)+~P9(f52(x5756,x5753,x5755,a57),x5751,x5757)+~E(f53(x5754,x5755),a63)+~P35(f42(a5,x5752))+~P35(f42(a5,x5751))+P35(f42(a5,f42(f42(f42(a20,x5751),x5752),x5753))) % 0.60/0.72 [576]~P9(x5766,x5762,x5764)+~P9(f52(x5766,x5763,x5764,a57),x5761,x5767)+~E(f53(x5764,x5765),a63)+~P35(f42(a5,x5762))+~P35(f42(a5,x5761))+P35(f42(a5,f42(f42(f42(a20,x5761),x5762),x5763))) % 0.60/0.72 %EqnAxiom % 0.60/0.72 [1]E(x11,x11) % 0.60/0.72 [2]E(x22,x21)+~E(x21,x22) % 0.60/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.60/0.72 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 0.60/0.72 [5]~E(x51,x52)+E(f38(x51,x53),f38(x52,x53)) % 0.60/0.72 [6]~E(x61,x62)+E(f38(x63,x61),f38(x63,x62)) % 0.60/0.72 [7]~E(x71,x72)+E(f37(x71,x73,x74,x75,x76),f37(x72,x73,x74,x75,x76)) % 0.60/0.72 [8]~E(x81,x82)+E(f37(x83,x81,x84,x85,x86),f37(x83,x82,x84,x85,x86)) % 0.60/0.72 [9]~E(x91,x92)+E(f37(x93,x94,x91,x95,x96),f37(x93,x94,x92,x95,x96)) % 0.60/0.72 [10]~E(x101,x102)+E(f37(x103,x104,x105,x101,x106),f37(x103,x104,x105,x102,x106)) % 0.60/0.72 [11]~E(x111,x112)+E(f37(x113,x114,x115,x116,x111),f37(x113,x114,x115,x116,x112)) % 0.60/0.72 [12]~E(x121,x122)+E(f42(x121,x123),f42(x122,x123)) % 0.60/0.72 [13]~E(x131,x132)+E(f42(x133,x131),f42(x133,x132)) % 0.60/0.72 [14]~E(x141,x142)+E(f34(x141,x143,x144),f34(x142,x143,x144)) % 0.60/0.72 [15]~E(x151,x152)+E(f34(x153,x151,x154),f34(x153,x152,x154)) % 0.60/0.72 [16]~E(x161,x162)+E(f34(x163,x164,x161),f34(x163,x164,x162)) % 0.60/0.72 [17]~E(x171,x172)+E(f10(x171),f10(x172)) % 0.60/0.72 [18]~E(x181,x182)+E(f11(x181),f11(x182)) % 0.60/0.72 [19]~E(x191,x192)+E(f41(x191,x193),f41(x192,x193)) % 0.60/0.72 [20]~E(x201,x202)+E(f41(x203,x201),f41(x203,x202)) % 0.60/0.72 [21]~E(x211,x212)+E(f17(x211,x213,x214,x215,x216),f17(x212,x213,x214,x215,x216)) % 0.60/0.72 [22]~E(x221,x222)+E(f17(x223,x221,x224,x225,x226),f17(x223,x222,x224,x225,x226)) % 0.60/0.72 [23]~E(x231,x232)+E(f17(x233,x234,x231,x235,x236),f17(x233,x234,x232,x235,x236)) % 0.60/0.72 [24]~E(x241,x242)+E(f17(x243,x244,x245,x241,x246),f17(x243,x244,x245,x242,x246)) % 0.60/0.72 [25]~E(x251,x252)+E(f17(x253,x254,x255,x256,x251),f17(x253,x254,x255,x256,x252)) % 0.60/0.72 [26]~E(x261,x262)+E(f52(x261,x263,x264,x265),f52(x262,x263,x264,x265)) % 0.60/0.72 [27]~E(x271,x272)+E(f52(x273,x271,x274,x275),f52(x273,x272,x274,x275)) % 0.60/0.72 [28]~E(x281,x282)+E(f52(x283,x284,x281,x285),f52(x283,x284,x282,x285)) % 0.60/0.72 [29]~E(x291,x292)+E(f52(x293,x294,x295,x291),f52(x293,x294,x295,x292)) % 0.60/0.72 [30]~E(x301,x302)+E(f4(x301,x303),f4(x302,x303)) % 0.60/0.72 [31]~E(x311,x312)+E(f4(x313,x311),f4(x313,x312)) % 0.60/0.72 [32]~E(x321,x322)+E(f6(x321),f6(x322)) % 0.60/0.72 [33]~E(x331,x332)+E(f51(x331),f51(x332)) % 0.60/0.72 [34]~E(x341,x342)+E(f7(x341),f7(x342)) % 0.60/0.72 [35]~E(x351,x352)+E(f35(x351,x353,x354),f35(x352,x353,x354)) % 0.60/0.72 [36]~E(x361,x362)+E(f35(x363,x361,x364),f35(x363,x362,x364)) % 0.60/0.72 [37]~E(x371,x372)+E(f35(x373,x374,x371),f35(x373,x374,x372)) % 0.60/0.72 [38]~E(x381,x382)+E(f49(x381,x383,x384),f49(x382,x383,x384)) % 0.60/0.72 [39]~E(x391,x392)+E(f49(x393,x391,x394),f49(x393,x392,x394)) % 0.60/0.72 [40]~E(x401,x402)+E(f49(x403,x404,x401),f49(x403,x404,x402)) % 0.60/0.72 [41]~E(x411,x412)+E(f48(x411,x413),f48(x412,x413)) % 0.60/0.72 [42]~E(x421,x422)+E(f48(x423,x421),f48(x423,x422)) % 0.60/0.72 [43]~E(x431,x432)+E(f33(x431,x433,x434),f33(x432,x433,x434)) % 0.60/0.72 [44]~E(x441,x442)+E(f33(x443,x441,x444),f33(x443,x442,x444)) % 0.60/0.72 [45]~E(x451,x452)+E(f33(x453,x454,x451),f33(x453,x454,x452)) % 0.60/0.72 [46]~E(x461,x462)+E(f28(x461,x463),f28(x462,x463)) % 0.60/0.72 [47]~E(x471,x472)+E(f28(x473,x471),f28(x473,x472)) % 0.60/0.72 [48]~E(x481,x482)+E(f12(x481),f12(x482)) % 0.60/0.72 [49]~E(x491,x492)+E(f29(x491,x493,x494),f29(x492,x493,x494)) % 0.60/0.72 [50]~E(x501,x502)+E(f29(x503,x501,x504),f29(x503,x502,x504)) % 0.60/0.72 [51]~E(x511,x512)+E(f29(x513,x514,x511),f29(x513,x514,x512)) % 0.60/0.72 [52]~E(x521,x522)+E(f54(x521,x523),f54(x522,x523)) % 0.60/0.72 [53]~E(x531,x532)+E(f54(x533,x531),f54(x533,x532)) % 0.60/0.72 [54]~E(x541,x542)+E(f32(x541,x543,x544),f32(x542,x543,x544)) % 0.60/0.72 [55]~E(x551,x552)+E(f32(x553,x551,x554),f32(x553,x552,x554)) % 0.60/0.72 [56]~E(x561,x562)+E(f32(x563,x564,x561),f32(x563,x564,x562)) % 0.60/0.72 [57]~E(x571,x572)+E(f36(x571,x573),f36(x572,x573)) % 0.60/0.72 [58]~E(x581,x582)+E(f36(x583,x581),f36(x583,x582)) % 0.60/0.72 [59]~E(x591,x592)+E(f43(x591,x593),f43(x592,x593)) % 0.60/0.72 [60]~E(x601,x602)+E(f43(x603,x601),f43(x603,x602)) % 0.60/0.72 [61]~E(x611,x612)+E(f40(x611,x613,x614,x615),f40(x612,x613,x614,x615)) % 0.60/0.72 [62]~E(x621,x622)+E(f40(x623,x621,x624,x625),f40(x623,x622,x624,x625)) % 0.60/0.72 [63]~E(x631,x632)+E(f40(x633,x634,x631,x635),f40(x633,x634,x632,x635)) % 0.60/0.72 [64]~E(x641,x642)+E(f40(x643,x644,x645,x641),f40(x643,x644,x645,x642)) % 0.60/0.72 [65]~E(x651,x652)+E(f19(x651,x653,x654),f19(x652,x653,x654)) % 0.60/0.72 [66]~E(x661,x662)+E(f19(x663,x661,x664),f19(x663,x662,x664)) % 0.60/0.72 [67]~E(x671,x672)+E(f19(x673,x674,x671),f19(x673,x674,x672)) % 0.60/0.72 [68]~E(x681,x682)+E(f45(x681,x683,x684,x685,x686),f45(x682,x683,x684,x685,x686)) % 0.60/0.72 [69]~E(x691,x692)+E(f45(x693,x691,x694,x695,x696),f45(x693,x692,x694,x695,x696)) % 0.60/0.72 [70]~E(x701,x702)+E(f45(x703,x704,x701,x705,x706),f45(x703,x704,x702,x705,x706)) % 0.60/0.72 [71]~E(x711,x712)+E(f45(x713,x714,x715,x711,x716),f45(x713,x714,x715,x712,x716)) % 0.60/0.72 [72]~E(x721,x722)+E(f45(x723,x724,x725,x726,x721),f45(x723,x724,x725,x726,x722)) % 0.60/0.72 [73]~E(x731,x732)+E(f59(x731,x733),f59(x732,x733)) % 0.60/0.72 [74]~E(x741,x742)+E(f59(x743,x741),f59(x743,x742)) % 0.60/0.72 [75]~E(x751,x752)+E(f53(x751,x753),f53(x752,x753)) % 0.60/0.72 [76]~E(x761,x762)+E(f53(x763,x761),f53(x763,x762)) % 0.60/0.72 [77]~E(x771,x772)+E(f26(x771),f26(x772)) % 0.60/0.72 [78]~E(x781,x782)+E(f30(x781,x783,x784),f30(x782,x783,x784)) % 0.60/0.72 [79]~E(x791,x792)+E(f30(x793,x791,x794),f30(x793,x792,x794)) % 0.60/0.72 [80]~E(x801,x802)+E(f30(x803,x804,x801),f30(x803,x804,x802)) % 0.60/0.72 [81]~E(x811,x812)+E(f22(x811,x813,x814),f22(x812,x813,x814)) % 0.60/0.72 [82]~E(x821,x822)+E(f22(x823,x821,x824),f22(x823,x822,x824)) % 0.60/0.72 [83]~E(x831,x832)+E(f22(x833,x834,x831),f22(x833,x834,x832)) % 0.60/0.72 [84]~E(x841,x842)+E(f39(x841,x843,x844),f39(x842,x843,x844)) % 0.60/0.72 [85]~E(x851,x852)+E(f39(x853,x851,x854),f39(x853,x852,x854)) % 0.60/0.72 [86]~E(x861,x862)+E(f39(x863,x864,x861),f39(x863,x864,x862)) % 0.60/0.72 [87]~E(x871,x872)+E(f15(x871,x873,x874),f15(x872,x873,x874)) % 0.60/0.72 [88]~E(x881,x882)+E(f15(x883,x881,x884),f15(x883,x882,x884)) % 0.60/0.72 [89]~E(x891,x892)+E(f15(x893,x894,x891),f15(x893,x894,x892)) % 0.60/0.72 [90]~E(x901,x902)+E(f8(x901,x903,x904,x905,x906),f8(x902,x903,x904,x905,x906)) % 0.60/0.72 [91]~E(x911,x912)+E(f8(x913,x911,x914,x915,x916),f8(x913,x912,x914,x915,x916)) % 0.60/0.72 [92]~E(x921,x922)+E(f8(x923,x924,x921,x925,x926),f8(x923,x924,x922,x925,x926)) % 0.60/0.72 [93]~E(x931,x932)+E(f8(x933,x934,x935,x931,x936),f8(x933,x934,x935,x932,x936)) % 0.60/0.72 [94]~E(x941,x942)+E(f8(x943,x944,x945,x946,x941),f8(x943,x944,x945,x946,x942)) % 0.60/0.72 [95]~E(x951,x952)+E(f47(x951,x953,x954),f47(x952,x953,x954)) % 0.60/0.72 [96]~E(x961,x962)+E(f47(x963,x961,x964),f47(x963,x962,x964)) % 0.60/0.72 [97]~E(x971,x972)+E(f47(x973,x974,x971),f47(x973,x974,x972)) % 0.60/0.72 [98]~E(x981,x982)+E(f23(x981,x983,x984),f23(x982,x983,x984)) % 0.60/0.72 [99]~E(x991,x992)+E(f23(x993,x991,x994),f23(x993,x992,x994)) % 0.60/0.72 [100]~E(x1001,x1002)+E(f23(x1003,x1004,x1001),f23(x1003,x1004,x1002)) % 0.60/0.72 [101]~E(x1011,x1012)+E(f58(x1011),f58(x1012)) % 0.60/0.72 [102]~E(x1021,x1022)+E(f18(x1021,x1023,x1024,x1025,x1026),f18(x1022,x1023,x1024,x1025,x1026)) % 0.60/0.72 [103]~E(x1031,x1032)+E(f18(x1033,x1031,x1034,x1035,x1036),f18(x1033,x1032,x1034,x1035,x1036)) % 0.60/0.72 [104]~E(x1041,x1042)+E(f18(x1043,x1044,x1041,x1045,x1046),f18(x1043,x1044,x1042,x1045,x1046)) % 0.60/0.72 [105]~E(x1051,x1052)+E(f18(x1053,x1054,x1055,x1051,x1056),f18(x1053,x1054,x1055,x1052,x1056)) % 0.60/0.72 [106]~E(x1061,x1062)+E(f18(x1063,x1064,x1065,x1066,x1061),f18(x1063,x1064,x1065,x1066,x1062)) % 0.60/0.72 [107]~E(x1071,x1072)+E(f44(x1071,x1073,x1074),f44(x1072,x1073,x1074)) % 0.60/0.72 [108]~E(x1081,x1082)+E(f44(x1083,x1081,x1084),f44(x1083,x1082,x1084)) % 0.60/0.72 [109]~E(x1091,x1092)+E(f44(x1093,x1094,x1091),f44(x1093,x1094,x1092)) % 0.60/0.72 [110]~E(x1101,x1102)+E(f24(x1101,x1103,x1104),f24(x1102,x1103,x1104)) % 0.60/0.72 [111]~E(x1111,x1112)+E(f24(x1113,x1111,x1114),f24(x1113,x1112,x1114)) % 0.60/0.72 [112]~E(x1121,x1122)+E(f24(x1123,x1124,x1121),f24(x1123,x1124,x1122)) % 0.60/0.72 [113]~E(x1131,x1132)+E(f27(x1131,x1133,x1134,x1135),f27(x1132,x1133,x1134,x1135)) % 0.60/0.72 [114]~E(x1141,x1142)+E(f27(x1143,x1141,x1144,x1145),f27(x1143,x1142,x1144,x1145)) % 0.60/0.72 [115]~E(x1151,x1152)+E(f27(x1153,x1154,x1151,x1155),f27(x1153,x1154,x1152,x1155)) % 0.60/0.72 [116]~E(x1161,x1162)+E(f27(x1163,x1164,x1165,x1161),f27(x1163,x1164,x1165,x1162)) % 0.60/0.72 [117]~E(x1171,x1172)+E(f31(x1171,x1173,x1174),f31(x1172,x1173,x1174)) % 0.60/0.72 [118]~E(x1181,x1182)+E(f31(x1183,x1181,x1184),f31(x1183,x1182,x1184)) % 0.60/0.72 [119]~E(x1191,x1192)+E(f31(x1193,x1194,x1191),f31(x1193,x1194,x1192)) % 0.60/0.72 [120]~E(x1201,x1202)+E(f46(x1201,x1203,x1204,x1205,x1206),f46(x1202,x1203,x1204,x1205,x1206)) % 0.60/0.72 [121]~E(x1211,x1212)+E(f46(x1213,x1211,x1214,x1215,x1216),f46(x1213,x1212,x1214,x1215,x1216)) % 0.60/0.72 [122]~E(x1221,x1222)+E(f46(x1223,x1224,x1221,x1225,x1226),f46(x1223,x1224,x1222,x1225,x1226)) % 0.60/0.72 [123]~E(x1231,x1232)+E(f46(x1233,x1234,x1235,x1231,x1236),f46(x1233,x1234,x1235,x1232,x1236)) % 0.60/0.72 [124]~E(x1241,x1242)+E(f46(x1243,x1244,x1245,x1246,x1241),f46(x1243,x1244,x1245,x1246,x1242)) % 0.60/0.72 [125]~E(x1251,x1252)+E(f50(x1251,x1253,x1254,x1255),f50(x1252,x1253,x1254,x1255)) % 0.60/0.72 [126]~E(x1261,x1262)+E(f50(x1263,x1261,x1264,x1265),f50(x1263,x1262,x1264,x1265)) % 0.60/0.72 [127]~E(x1271,x1272)+E(f50(x1273,x1274,x1271,x1275),f50(x1273,x1274,x1272,x1275)) % 0.60/0.72 [128]~E(x1281,x1282)+E(f50(x1283,x1284,x1285,x1281),f50(x1283,x1284,x1285,x1282)) % 0.60/0.72 [129]~E(x1291,x1292)+E(f21(x1291,x1293),f21(x1292,x1293)) % 0.60/0.72 [130]~E(x1301,x1302)+E(f21(x1303,x1301),f21(x1303,x1302)) % 0.60/0.72 [131]~E(x1311,x1312)+E(f9(x1311,x1313),f9(x1312,x1313)) % 0.60/0.72 [132]~E(x1321,x1322)+E(f9(x1323,x1321),f9(x1323,x1322)) % 0.60/0.72 [133]~E(x1331,x1332)+E(f25(x1331),f25(x1332)) % 0.60/0.72 [134]~P1(x1341)+P1(x1342)+~E(x1341,x1342) % 0.60/0.72 [135]P9(x1352,x1353,x1354)+~E(x1351,x1352)+~P9(x1351,x1353,x1354) % 0.60/0.72 [136]P9(x1363,x1362,x1364)+~E(x1361,x1362)+~P9(x1363,x1361,x1364) % 0.60/0.72 [137]P9(x1373,x1374,x1372)+~E(x1371,x1372)+~P9(x1373,x1374,x1371) % 0.60/0.72 [138]~P2(x1381)+P2(x1382)+~E(x1381,x1382) % 0.60/0.72 [139]~P35(x1391)+P35(x1392)+~E(x1391,x1392) % 0.60/0.72 [140]~P24(x1401)+P24(x1402)+~E(x1401,x1402) % 0.60/0.73 [141]~P25(x1411)+P25(x1412)+~E(x1411,x1412) % 0.60/0.73 [142]~P3(x1421)+P3(x1422)+~E(x1421,x1422) % 0.60/0.73 [143]~P4(x1431)+P4(x1432)+~E(x1431,x1432) % 0.60/0.73 [144]~P5(x1441)+P5(x1442)+~E(x1441,x1442) % 0.60/0.73 [145]~P22(x1451)+P22(x1452)+~E(x1451,x1452) % 0.60/0.73 [146]~P6(x1461)+P6(x1462)+~E(x1461,x1462) % 0.60/0.73 [147]~P17(x1471)+P17(x1472)+~E(x1471,x1472) % 0.60/0.73 [148]~P26(x1481)+P26(x1482)+~E(x1481,x1482) % 0.60/0.73 [149]~P34(x1491)+P34(x1492)+~E(x1491,x1492) % 0.60/0.73 [150]~P28(x1501)+P28(x1502)+~E(x1501,x1502) % 0.60/0.73 [151]~P29(x1511)+P29(x1512)+~E(x1511,x1512) % 0.60/0.73 [152]~P27(x1521)+P27(x1522)+~E(x1521,x1522) % 0.60/0.73 [153]~P18(x1531)+P18(x1532)+~E(x1531,x1532) % 0.60/0.73 [154]~P19(x1541)+P19(x1542)+~E(x1541,x1542) % 0.60/0.73 [155]~P32(x1551)+P32(x1552)+~E(x1551,x1552) % 0.60/0.73 [156]~P21(x1561)+P21(x1562)+~E(x1561,x1562) % 0.60/0.73 [157]~P7(x1571)+P7(x1572)+~E(x1571,x1572) % 0.60/0.73 [158]~P8(x1581)+P8(x1582)+~E(x1581,x1582) % 0.60/0.73 [159]~P23(x1591)+P23(x1592)+~E(x1591,x1592) % 0.60/0.73 [160]P15(x1602,x1603,x1604)+~E(x1601,x1602)+~P15(x1601,x1603,x1604) % 0.60/0.73 [161]P15(x1613,x1612,x1614)+~E(x1611,x1612)+~P15(x1613,x1611,x1614) % 0.60/0.73 [162]P15(x1623,x1624,x1622)+~E(x1621,x1622)+~P15(x1623,x1624,x1621) % 0.60/0.73 [163]P11(x1632,x1633,x1634)+~E(x1631,x1632)+~P11(x1631,x1633,x1634) % 0.60/0.73 [164]P11(x1643,x1642,x1644)+~E(x1641,x1642)+~P11(x1643,x1641,x1644) % 0.60/0.73 [165]P11(x1653,x1654,x1652)+~E(x1651,x1652)+~P11(x1653,x1654,x1651) % 0.60/0.73 [166]P10(x1662,x1663,x1664)+~E(x1661,x1662)+~P10(x1661,x1663,x1664) % 0.60/0.73 [167]P10(x1673,x1672,x1674)+~E(x1671,x1672)+~P10(x1673,x1671,x1674) % 0.60/0.73 [168]P10(x1683,x1684,x1682)+~E(x1681,x1682)+~P10(x1683,x1684,x1681) % 0.60/0.73 [169]P12(x1692,x1693)+~E(x1691,x1692)+~P12(x1691,x1693) % 0.60/0.73 [170]P12(x1703,x1702)+~E(x1701,x1702)+~P12(x1703,x1701) % 0.60/0.73 [171]~P20(x1711)+P20(x1712)+~E(x1711,x1712) % 0.60/0.73 [172]~P31(x1721)+P31(x1722)+~E(x1721,x1722) % 0.60/0.73 [173]~P30(x1731)+P30(x1732)+~E(x1731,x1732) % 0.60/0.73 [174]~P16(x1741)+P16(x1742)+~E(x1741,x1742) % 0.60/0.73 [175]P13(x1752,x1753,x1754)+~E(x1751,x1752)+~P13(x1751,x1753,x1754) % 0.60/0.73 [176]P13(x1763,x1762,x1764)+~E(x1761,x1762)+~P13(x1763,x1761,x1764) % 0.60/0.73 [177]P13(x1773,x1774,x1772)+~E(x1771,x1772)+~P13(x1773,x1774,x1771) % 0.60/0.73 [178]~P14(x1781)+P14(x1782)+~E(x1781,x1782) % 0.60/0.73 [179]~P33(x1791)+P33(x1792)+~E(x1791,x1792) % 0.60/0.73 % 0.60/0.73 %------------------------------------------- % 0.60/0.73 cnf(680,plain, % 0.60/0.73 ($false), % 0.60/0.73 inference(scs_inference,[],[287,340,631]), % 0.60/0.73 ['proof']). % 0.60/0.73 % SZS output end Proof % 0.60/0.73 % Total time :0.023605s %------------------------------------------------------------------------------